Regression analysis and hypothesis testing

Question

During a research study, a random sample of eight drivers insured with a Flamingo Group Insurance and having similar auto insurance policies was chosen. The following data reveals their driving experiences (in years) () and monthly auto insurance premiums (). Driving Experience (years) 5 2 12 9 15 6 25 16 Monthly Auto Insurance Premium ($) 65 88 55 72 47 59 44 65 (a) Draw a scatter diagram on graph paper to represent the above information and comment on what the diagram indicates. [1] (b) Find the equation of the regression line of  =  + . Draw this line on the same scatter diagram. [2] (c) Interpret the regression equation obtained in part (b). [1] (d) Compute the correlation coefficient for the above data and interpret the result. [1] (e) Compute the coefficient of determination for the above data and interpret the result. [1] (f) Obtain an estimate of the monthly auto insurance premium with driving experience of (i) 13 years (ii) 30 years Comment on the reliability of the two estimates. [1] (g) Assuming a linear regression model,  =  +  +  . Calculate a 95% confidence interval for  assuming  ~ N (0,  2 ). Would you reject the hypothesis that  = 0 at the 1% level of significance?