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AP Statistics Page 1 of5 Ch 3 Aim 9: Review for Test on Linear Regression Exainple 1: A study comparing car life (in years) to purchase price of the car (in dollars) was conducted using 11 randomly selected American-made cars. Using a statistical software program, a least squares regression line was fit to the data and yielded the following printout: Dependent variable is: Life No Selector R squared = 50.2 % R squared (adjusted) = 44.6 9/~ s = 1.149 with 11 - 2 = 9 degrees of freedom Source Sum of Squares df Mean Square f-ratio Regression 11.9633 1 11.9633 9.06 Residual 11.884 9 1.32045 Variable Coefficient SE of Coeff t-ratlo Prob Constant 0.935199 1.153 0.811 0.4382 Cost 0.000163839 0.00005443 3.01 0.0147 A. What is the regression equation? B. Interpret the slope of the regression line in the context of the study. The residual plot for this regression is displayed below: • 1.50 '- • 'I 0.75- _I 0- • •• • -G.76r- • • I I I- . "" I a 4 5 6 PIadicIed C. Comment on the goodness of fit of the model to-the data. Explain your reasoning. D. Estimate the approximate life ofa-car in the sample whose purchase price is $18,500. E. Does this model overestimate or underestimate the actual life of the car in part d? Explain the reasons for your answer. Solution: A. Y = 0.000163839 x + 0.935199 life of car in years = 0.000163839 (cost of car) + 0.935199 0.000163839 change in life B. I sope =----- 1 change in cost __O. 163839 __ ch.ange in life slope (Multiply numerator and denominator by 1000) 1000 change in cost If the cost of the car increases by $1000, the life of the car increases by approximately 0.164 years. C. A linear tnociei appears appropriate since the residual plot is a random scattering of points with no clear pattern. ©copyright AP Statistics Page z of S Ch 3 Aim 9: Review for Test on Linear Regression D. x = 18500when the cost of the car is $18,500 9 = 0.000163839 (18500)+0.935199 9 = 3.966 The life of the car is approximately 4 years. E. The residuals in the residual plot are negative for predicted values between 3.4 years and 4.2 years. It is likely that the residual for a predicted value of 4 years would also have a negative residual. Since residual = predicted value -observed value, the predicted value would be more than the actual value, and the model overestimates the life of the car. Example 2: AI- Statistics 2003 Free RespoBse QUestiOBS,FOnD B, Problem 1 A simple random sample of 9 students was selected from a large university. Each of these students reported the number of hours he or she bad allocated to studying and the number of hours allocated to work each week. A least squares linear regression was performed and part of the resulting computer output is shown below. Predictor Coef StDev

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