Question

3. The regional transit authority for a major metropolitan area wants to determine whether there is w e ar relationship between the mileage of a bus and the market resale value of the bus. A very small random sample! resulted in the following data Bus Mileage Resale Value (in 1000 of Miles)__(in $1000) a. Use the method of OLS to compute the slope and intercept of sample linear regression line. You need to decide which one is the dependent variable. In addition, write down the estimated sample regression line Show all of your computations, b. Explain the meaning of estimated sample intercept and slope in the context of this problem and in plain English c. Use a level of significance of 0.05 to check if the population slope is statistically equal to or different from

Answer 1

Bus Mileage (Y). را در 0 09 0 Resale Value xy x² 42 58 290 25 3364 Ex²= 104 270 8100 85 3y2 =35250 340 7225 96 192 9216 exy = 1697. 64 25 320 4096 57 - 285 3249 EY= 450 1697 104 35250 0 = Ey دل ای OU ) X = 242 X = {X = 24 Y = {y M <X2 n 5 © =4 Vy = 3y2 -12 vñ 575 12 se trou-uh o le - 16 V 6 35250 - 757 -14547 r = {xy _ x 54 - 15.811 n оя - бу = 1697_4X75 1-1547 X15.81 - - 0.9402 a) Since Resale value of Bus is dependent on Bus Mileage, Resale value is dependent Variable & Bus Mileage is Independent variable. Slope - byx arx y = -0.9402 x 15.811 = -12.874 Fa 1.1547 RI Intercept = 7 - (byx x x = 75 + 12.874x4 = 126.50

line is Estimated sample regression Y = 126.50 - 12.874 (X) b] Value of Intercept indicates that Value of y, when x=o. ie what will be resale Value when bus Mileage is zero? But zero Bus Mileage is not possible. So this interpretation doesn't make sense in this example. slope indicates change in dependent Variable when independent Variable changes by 1 unit. Here 1 unit = 1000 miles... so, when Bus Mileage changes by 1000 miles Resale Value of Bus will change by $ 12874. (decrease) Negative Value of slope indicates that as x increases y decreases inverse proportion). c Ho: b=o (Bus Mileage doesn't play Significant Role in predicting y) Hib o (Bus Mileage play's significant role in predicting Resale value) Test-statistic: t=b/s.Elb) ntn. Since there is only one Independent Variable se(b)= (-12) xey n-2 =-12.874 2.3321 = - 5. 5203 Sy voy? (1-x2) = 5-386 sx = Vox? (1-82) = 0.3933 Selb) = 1-(-0-9402)2 x 5:30 0-11602 x 5.386 = 2.33 0-3933 6-2 0.3933

0.05 (two sided) critical t-value at level of significance at dit 4 is tcri = 2.776 since Itcal /> tori, We Reject Ho at 5% level of significance. & Conclude that Bus Mileage plays significant role in predicting Resale Value. - 5.52 - 2.776 dj coefficient of determination = $= (-0.9402) - 0.8839. price can 88.39% of be explained Variation is value of Resale by Regression model.