7. Data were collected to predict the number of students enrolling in a college in the Autumn (ROLL), using the local unemployment rate (UNE, %), the number of students completing high school locally (HGRAD) and the per capita income in the local area (INC, ). A linear model was fitted using R and the following output was obtained Call: lm(formula = ROLL ~ UNEM + HGRAD + INC) Residuals: Min 1QMedian 3Q 1148.84 -489.71 1.88 387.40 1425.75 Coefficients: Estimate Std. Error t value Pr(>ltI) (Intercept) -9.153e+03 1.053e+03 -8.691 5.02e-09** UNEM HGRAD INC 4.501e+02 1.182e+02 4.065-01 7.602-02 4.275+00 4.947-01 3.809 0.000807 5.347 1.52-05 8.642 5.59-09 Signif. codes: 0*0.001 ** 0.01 * 0.05 . 0.1 1 Residual standard error 670.4 on 25 degrees of freedom Multiple R-squared: 0.9621,Adjusted R-squared: 0.9576 F-statistic: 211.5 on 3 and 25 DF, p-value: > INC (Intercept) 1654.41653470 -1.247456e+02 -2.779806e-02 -0.0766284838 -124.74556008 2.082760e+01 1.321497e-03 -0.0211864043 0.02779806 1.321497e-03 8.619370e-06 -0.0000457458 -0.07662848-2.118640e-02 -4.574580e-05 0.0003649857 (Intercept) HGRAD UNEM UNEM HGRAD INC Obtain a 99% prediction interval for a year in which the unemployment and the per capita income is 3350. [10 marks] marks] (c) Suggest what further analysis should be performed, giving reasons. [5 7. Data were collected to predict the number of students enrolling in a college in the Autumn (ROLL), using the local unemployment rate (UNE, %), the number of students completing high school locally (HGRAD) and the per capita income in the local area (INC, ). A linear model was fitted using R and the following output was obtained Call: lm(formula = ROLL ~ UNEM + HGRAD + INC) Residuals: Min 1QMedian 3Q 1148.84 -489.71 1.88 387.40 1425.75 Coefficients: Estimate Std. Error t value Pr(>ltI) (Intercept) -9.153e+03 1.053e+03 -8.691 5.02e-09** UNEM HGRAD INC 4.501e+02 1.182e+02 4.065-01 7.602-02 4.275+00 4.947-01 3.809 0.000807 5.347 1.52-05 8.642 5.59-09 Signif. codes: 0*0.001 ** 0.01 * 0.05 . 0.1 1 Residual standard error 670.4 on 25 degrees of freedom Multiple R-squared: 0.9621,Adjusted R-squared: 0.9576 F-statistic: 211.5 on 3 and 25 DF, p-value: > INC (Intercept) 1654.41653470 -1.247456e+02 -2.779806e-02 -0.0766284838 -124.74556008 2.082760e+01 1.321497e-03 -0.0211864043 0.02779806 1.321497e-03 8.619370e-06 -0.0000457458 -0.07662848-2.118640e-02 -4.574580e-05 0.0003649857 (Intercept) HGRAD UNEM UNEM HGRAD INC Obtain a 99% prediction interval for a year in which the unemployment and the per capita income is 3350. [10 marks] marks] (c) Suggest what further analysis should be performed, giving reasons. [5