## Question

###### Problem 3. (20 points) An engineer would like to use simple linear regression to investigate the relationship between roadway surface temperature in % (x) and pavement deflection (y). A sample of n-20 pairs of observations was obtained and the following summary quantities were calculated: Zyi 12.75,Zy? =8.86,Ex;1478,Ex} =143,215.8,and Exv;-1083.67 (all summations are for i = 1...n)-Find the least-squares estimates of the slope and the intercept_ Assess the utility of the model by formulating and

Problem 3. (20 points) An engineer would like to use simple linear regression to investigate the relationship between roadway surface temperature in % (x) and pavement deflection (y). A sample of n-20 pairs of observations was obtained and the following summary quantities were calculated: Zyi 12.75,Zy? =8.86,Ex;1478,Ex} =143,215.8,and Exv;-1083.67 (all summations are for i = 1...n)- Find the least-squares estimates of the slope and the intercept_ Assess the utility of the model by formulating and testing an appropriate hypothesis regarding the slope parameter: Use &-0.05. Report the p-value corresponding to this test: What is your conclusion? {C) What change in mean pavement deflection would be expected for 5F increase in surface temperature? (d) What is the predicted value of pavement deflection when the surface temperature is 859F? What is the respective 95% prediction interval?