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Homework answers / question archive / Math 142 classwork 12

Math 142 classwork 12.1, 3 and 12.5 1) Which of the following equation represents a line with positive slope? a) y = -3x - 1 b) y = -x +4 c) y = 0.2x - 7 2) Ethan repairs household appliances like dishwashers and refrigerators. For each visit, he charges $35 plus $30 per hour of work. A linear equation that expresses the total amount of money Ethan earns per visit can be which equation? a) y = 30 + 35 x b) y = 35 + 30 x c) y = - 30 + 35 x What is the independent variable? What is the dependent variable? What is the slope? Interpret the meaning of the slope. What is the y-intercept? Interpret the meaning of the y-intercept. 18.0 3) Given the following matched-pair data: 20.0 17.0 12.0 10.0 ly 68.0 75.00 60.0 50.00 47.0 a) Use Statdisk to find the linear regression line equation. Round coefficient to 3 decimal places. b) Check scatter plot for any non-linear pattern or outliers c) Use r or p-value to determine if there is evidence of linear correlation. Use a = 0.05. d) What is the best predicted value given x = 132. Explain if you will use linear equation or y for prediction. e) Find r and give an interpretation of r. 4) In a study to determine the relationship between ambient outdoor temperature and the rate of evaporation of water from soil, measurements of average daytime temperature in °C and evaporation in millimeters per day were taken for 10 days. The results are show below: Temperature 11.8 21.5 16.5 23.6 19.1 21.6 31.0 18.9 24.2 19.1 Evaporation 2.4 4.45.0 4.1 6.0 5.9 4.8 3.0 7.1 1.6 a) Use Statdisk to find the linear regression line equation. 3 b) Check scatter plot for any non-linear pattern or outliers. c) Use r or p-value to determine if there is evidence of linear correlation. Use a significant level of 0.05. d) What is the best predicted evaporation value û when temperature is 24.2°C, round to 1 decimal place. Explain if you will use the linear equation or y for prediction. 5) A set of n = 10 paired data are collected from 10 job applicants. The sample mean years the applicant has studied German is 4.1 years and the sample mean German proficiency test score is 30.4. The matched pair gives a correlation coefficient r of 0.846 and a p-value of 0.006 at a significant level of 0.05. Linear regression equation is calculated as ? = 31.6+10.9x. Where x = the number of years that applicants have studied German and y = the score received on German proficiency test. a) Assume that scatter plot does not show non-linear patterns or outliers. Use correlation coefficient or p-value to determine if there is evidence of linear correlation between x and y. b) What is the best predicted value of proficiency test score for a student who has studied 3 years of German? 6) A random sample of heights (in inches) and pulse rate (in beats per min.) are obtained from 100 women. The sample mean height is 63.9 in. and sample mean pulse rate is 75.1 bpm. The linear correlation coefficient r is found to be 0.251 and p-value is 0.11. The linear regression line is ? = 18.5+0.88x where x represents heights, y represents pulse rate. Assume that scatter plot does not show non-linear patterns or outliers. a) Use the given correlation r or p-value, at a significant level of 0.01, are there linear correlation between x and y? b) Find the best predicted pulse rate of a woman who is 68 in. tall. (Round to 1 decimal place.) 7) The data below records the price in thousands of $) of a sample of houses sold in a city. These data were obtained from an internet real estate site. size(sq. ft) x 480 1916 1656 1796 951 2179 1083 796 1325 1402 1691 price ($1000) y 259 875 635 745 767 245 335 470 405 420 a) Find the equation of linear regression line. (Round to 3 decimal places) 480 4 b) Check scatter plot for non-linear pattern. Find p-value of linear regression test. Use a significant level of 0.05 to determine if there is evidence of linear correlation. c) Use the result in part b to find the best predicted value of price if the size of a house is 1325 sq.ft. (Round to nearest thousands.) d) Is the predicted price close to the actual price for a house of size 1325 sq ft.? e) Can we use the regression equation to predict the price of a house with size 4000 sq. ft? Why?

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