A study was conducted te understand the inuence of 1.raritnls factors. including parents background. test preparation etc. on students' performance. Date: on li} male and female students were collected. Firstly, we are interested in modelling mathematics score (math . score) as a function of reading score {reading . sco re}. A scatter plot is reproduced below. SCI ED 1E| merthscore 4D El] 40 Bi] 3!] 10'] leadingscore \f(c) [5 marks] Is the regression model statistically significant at the 0.05 level (the relevant quantiles are togo = 1.28, to.95 = 1.65, to.975 = 1.96, to995 = 2.58)? Write down the null and alternative hypotheses, calculate the test statistic, report the result of the chosen test and state a conclusion in plain English.A simple linear regression model was built with reading . score as the predictor variable and math. score as the response variable. Selected R output is displayed below. Coefficients : Estimate Std. Error t value Pr(>|t|) (Intercept) 7.35759 1. 33818 5.498 4.87e-08 *** reading . score 0. 84910 0. 01893 Signif. codes: 0 (***' 0. 001 (**' 0.01 (*' 0.05 ' . ' 0.1 ' ' 1 Residual standard error: 8.736 on 998 degrees of freedom Multiple R-squared: 0.6684, Adjusted R-squared: 0.6681In addition to the output above, R also produced the following residual plots and statistics. Normal P-P Plot 0.0 0.2 0.4 0.6 0.8 1.0 Expected Probability 0.0 0.2 0.4 0.6 0.8 1.0 Observed Probability 8 08 co bopop Standardised residuals 20 40 60 80 100 reading score> cooksD round ( summary ( cooksD ) , 3) Min. 1st Qu. Median Mean 3rd Qu. Max. 0. 000 0.000 0.000 0. 001 0. 001 0. 044 (d) [4 marks] Decide if the regression model can be relied upon. Justify your answer. (e) [2 marks] Using the output provided, determine if there is a potential problem with influential point(s). Provide reasons for your answer. (f) [2 marks] Calculate the 90% two-sided confidence interval for the slope parameter , (to.90 = 1.29, to.95 = 1.65, to.975 = 1.97, to.995 = 2.60)