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Question1)One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y)

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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.

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 Regression Statistics R Square 0.808 Observations 20 ANOVA df SS MS F Significance F Regression 4 169503.4241 42375.8600 15.7874 0.0000 Residual 15 40262.3259 2684.1550 Total 19 209765.7500 Coefficients Standard Error t Stat P-value Lower 90% Upper 90% Intercept 421.4277 77.8614 5.4125 0.0000 284.9327 557.9227 X1 (Temperature) -4.5098 0.8129 -5.5476 0.0000 -5.9349 -3.0847 X2 (Insulation) -14.9029 5.0508 -2.5905 0.0099 -23.7573 -6.0485 X3 (Windows) 0.2151 4.8675 0.0442 0.9653 -8.3181 8.7484 X4 (Furnace Age) 6.3780 4.1026 1.5546 0.1408 -0.8140 13.5702

According to these results, the proportion of variability in heating costs explained by the regression model is ________  ( use three decimals)

Question 2

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:

 Employee Y (\$) X1 X2 1 10 3 0 2 12 1 5 3 15 8 1 4 17 5 8 5 20 7 12 6 25 10 9

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)

Question 3

 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 ____________________

Question 4

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.

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 Student CoopJobs JobOffer 1 1 4 2 2 6 3 1 3 4 0 1

The standard error of the regression is  _________

Question 5

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

Standard Error 5.195

Observations 50

ANOVA

 df SS MS F Signif F Regression 3605.7736 1201.9245 0.0000 Residual 1214.2264 26.3962 Total 49 4820.0000

 Coeff StdError t Stat p-value Intercept -1.6335 5.8078 -0.281 0.7798 Income 0.4485 0.1137 3.9545 0.0003 Size 4.2615 0.8062 5.286 0.0001 School -0.6517 0.4319 -1.509 0.1383

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)

Question 6

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

 Multiple R 0.916 R Square ? Adjusted R Square 0.732 Standard Error 0.247 Observations 6

ANOVA

 df SS MS F Signif F Regression 2 0.95219 0.4761 7.813 0.0646 Residual 3 0.18281 0.06094 Total 5 1.135

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 Coeff StdError Intercept 4.593897 1.133742 Units -0.247270 0.062685 SAT Total 0.001443 0.001012

The value of the test statistic for the intercept of the regression line is ________ (use three decimals)

Question 7

 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  ________

Question 8

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.

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 Regression Statistics R Square 0.808 Adjusted R Square 0.7568 Observations 20 ANOVA df SS MS F Significance F Regression 4 169503.4241 42375.8600 15.7874 0.0000 Residual 15 40262.3259 2684.1550 Total 19 209765.7500 Coefficients Standard Error t Stat P-value Lower 90% Upper 90% Intercept 421.4277 77.8614 5.4125 0.0000 284.9327 557.9227 X1 (Temperature) -4.5098 0.8129 -5.5476 0.0000 -5.9349 -3.0847 X2 (Insulation) -14.9029 5.0508 -2.5905 0.0099 -23.7573 -6.0485 X3 (Windows) 0.2151 4.8675 0.0442 0.9653 -8.3181 8.7484 X4 (Furnace Age) 6.3780 4.1026 1.5546 0.1408 -0.8140 13.5702

The margin of error for a 99% confidence interval for the coefficient of Insulation is  ________

Question 9

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

 Multiple R 0.916 R Square ? Adjusted R Square 0.732 Standard Error 0.247 Observations 6

ANOVA

 df SS MS F Signif F Regression 2 0.95219 0.4761 7.813 0.0646 Residual 3 0.18281 0.06094 Total 5 1.135

 Coeff StdError Intercept 4.594 1.134 Units -0.247 0.063 SAT Total 0.001 0.001

The proportion of variability in the response variable explained by the regression model is ________ (use three decimals)

Question 10

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.

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 Regression Statistics R Square 0.808 Adjusted R Square 0.7568 Observations 20 ANOVA df SS MS F Significance F Regression 4 169503.4241 42375.8600 15.7874 0.0000 Residual 15 40262.3259 2684.1550 Total 19 209765.7500 Coefficients Standard Error t Stat P-value Lower 90% Upper 90% Intercept 421.4277 77.8614 5.4125 0.0000 284.9327 557.9227 X1 (Temperature) -4.5098 0.8129 -5.5476 0.0000 -5.9349 -3.0847 X2 (Insulation) -14.9029 5.0508 -2.5905 0.0099 -23.7573 -6.0485 X3 (Windows) 0.2151 4.8675 0.0442 0.9653 -8.3181 8.7484 X4 (Furnace Age) 6.3780 4.1026 1.5546 0.1408 -0.8140 13.5702

According to these results,  the coefficient for temperature is significant in predicting heating costs.

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