Question1)One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1) the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below is the Excel output for the regression model.
mso-para-margin-bottom:.0001pt; line-height:200%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}
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Regression Statistics
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R Square
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0.808
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Observations
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20
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ANOVA
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df
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SS
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MS
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F
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Significance F
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Regression
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4
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169503.4241
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42375.8600
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15.7874
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0.0000
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Residual
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15
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40262.3259
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2684.1550
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Total
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19
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209765.7500
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Coefficients
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Standard Error
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t Stat
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P-value
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Lower 90%
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Upper 90%
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Intercept
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421.4277
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77.8614
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5.4125
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0.0000
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284.9327
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557.9227
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X1 (Temperature)
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-4.5098
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0.8129
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-5.5476
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0.0000
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-5.9349
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-3.0847
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X2 (Insulation)
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-14.9029
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5.0508
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-2.5905
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0.0099
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-23.7573
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-6.0485
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X3 (Windows)
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0.2151
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4.8675
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0.0442
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0.9653
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-8.3181
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8.7484
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X4 (Furnace Age)
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6.3780
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4.1026
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1.5546
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0.1408
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-0.8140
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13.5702
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According to these results, the proportion of variability in heating costs explained by the regression model is ________ ( use three decimals)
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Question 2
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A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects 6 workers and collects the following information:
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Employee
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Y ($)
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X1
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X2
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1
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10
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3
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0
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2
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12
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1
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5
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3
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15
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8
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1
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4
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17
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5
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8
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5
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20
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7
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12
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6
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25
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10
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9
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Use this information to run a multiple regression in Excel. (you can try copying and pasting the table above so that you don't have to type in the numbers).
The margin of error for a 90% confidence interval of the intercept of the regression line is ___________________ (use three decimals)
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Question 3
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A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects 6 workers and collects information to build a regression model.
For this regression model, wage rate is ____________________
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Question 4
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The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place. She takes a random sample of 4 students. For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.
mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} table.MsoTableGrid {mso-style-name:"Table Grid"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-priority:59; mso-style-unhide:no; border:solid windowtext 1.0pt; mso-border-alt:solid windowtext .5pt; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-border-insideh:.5pt solid windowtext; mso-border-insidev:.5pt solid windowtext; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Calibri","sans-serif"; mso-bidi-font-family:"Times New Roman";}
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Student
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CoopJobs
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JobOffer
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1
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1
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4
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2
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2
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6
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3
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1
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3
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4
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0
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1
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The standard error of the regression is _________
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Question 5
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A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below
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Regression Statistics
Multiple R 0.865
R Square 0.748
Adjusted R Square 0.726
Standard Error 5.195
Observations 50
ANOVA
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df
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SS
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MS
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F
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Signif F
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Regression
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3605.7736
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1201.9245
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0.0000
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Residual
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1214.2264
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26.3962
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Total
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49
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4820.0000
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Coeff
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StdError
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t Stat
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p-value
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Intercept
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-1.6335
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5.8078
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-0.281
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0.7798
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Income
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0.4485
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0.1137
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3.9545
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0.0003
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Size
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4.2615
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0.8062
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5.286
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0.0001
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School
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-0.6517
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0.4319
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-1.509
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0.1383
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one individual in the sample had an annual income of $100,000, a family size of 10, and an education of 16 years. This individual owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet) for this data point? (use three decimals)
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Question 6
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The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft Excel output:
Summary Output - Regression Statistics
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Multiple R
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0.916
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R Square
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?
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Adjusted R Square
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0.732
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Standard Error
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0.247
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Observations
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6
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ANOVA
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df
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SS
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MS
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F
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Signif F
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Regression
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2
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0.95219
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0.4761
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7.813
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0.0646
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Residual
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3
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0.18281
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0.06094
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Total
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5
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1.135
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Coeff
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StdError
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Intercept
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4.593897
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1.133742
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Units
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-0.247270
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0.062685
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SAT Total
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0.001443
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0.001012
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The value of the test statistic for the intercept of the regression line is ________ (use three decimals)
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Question 7
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A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y)-measured in dollars per month-for services rendered to local companies. One independent variable used to predict service charges to a company is the company's sales revenue (X) -measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model. The results of the simple linear regression are provided below.
Y = -2,700 + 20X
According to these results, the error (residuals ) degrees of freedom for this model is ________
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Question 8
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One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1) the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below is the Excel output for the regression model.
mso-para-margin-bottom:.0001pt; line-height:200%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}
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Regression Statistics
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R Square
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0.808
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Adjusted R Square
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0.7568
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Observations
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20
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ANOVA
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df
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SS
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MS
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F
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Significance F
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Regression
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4
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169503.4241
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42375.8600
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15.7874
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0.0000
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Residual
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15
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40262.3259
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2684.1550
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Total
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19
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209765.7500
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Coefficients
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Standard Error
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t Stat
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P-value
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Lower 90%
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Upper 90%
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Intercept
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421.4277
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77.8614
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5.4125
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0.0000
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284.9327
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557.9227
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X1 (Temperature)
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-4.5098
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0.8129
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-5.5476
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0.0000
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-5.9349
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-3.0847
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X2 (Insulation)
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-14.9029
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5.0508
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-2.5905
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0.0099
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-23.7573
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-6.0485
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X3 (Windows)
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0.2151
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4.8675
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0.0442
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0.9653
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-8.3181
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8.7484
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X4 (Furnace Age)
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6.3780
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4.1026
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1.5546
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0.1408
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-0.8140
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13.5702
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The margin of error for a 99% confidence interval for the coefficient of Insulation is ________
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Question 9
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The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft Excel output:
Summary Output - Regression Statistics
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Multiple R
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0.916
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R Square
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?
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Adjusted R Square
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0.732
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Standard Error
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0.247
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Observations
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6
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ANOVA
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df
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SS
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MS
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F
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Signif F
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Regression
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2
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0.95219
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0.4761
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7.813
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0.0646
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Residual
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3
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0.18281
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0.06094
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Total
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5
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1.135
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Coeff
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StdError
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Intercept
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4.594
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1.134
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Units
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-0.247
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0.063
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SAT Total
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0.001
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0.001
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The proportion of variability in the response variable explained by the regression model is ________ (use three decimals)
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Question 10
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One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1) the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below is the Excel output for the regression model.
mso-para-margin-bottom:.0001pt; line-height:200%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}
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Regression Statistics
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R Square
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0.808
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Adjusted R Square
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0.7568
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Observations
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20
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ANOVA
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df
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SS
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MS
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F
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Significance F
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Regression
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4
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169503.4241
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42375.8600
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15.7874
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0.0000
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Residual
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15
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40262.3259
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2684.1550
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Total
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19
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209765.7500
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Coefficients
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Standard Error
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t Stat
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P-value
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Lower 90%
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Upper 90%
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Intercept
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421.4277
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77.8614
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5.4125
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0.0000
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284.9327
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557.9227
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X1 (Temperature)
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-4.5098
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0.8129
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-5.5476
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0.0000
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-5.9349
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-3.0847
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X2 (Insulation)
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-14.9029
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5.0508
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-2.5905
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0.0099
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-23.7573
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-6.0485
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X3 (Windows)
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0.2151
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4.8675
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0.0442
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0.9653
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-8.3181
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8.7484
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X4 (Furnace Age)
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6.3780
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4.1026
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1.5546
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0.1408
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-0.8140
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13.5702
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According to these results, the coefficient for temperature is significant in predicting heating costs.
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