Problem 5: R Problem 2 A data set contains Facebook Penetration and Internet penetration of 32 counties in 2012. We will use a regression model where y:percentage of Facebook users, 3: percentage of Internet users and conduct a hypothesis test for H 0 x3 : 0 against H a 6 : 0. (The complete data set is available at https:l/istats.shinyapps.io/LinearRegression/ Under Choose data set, click "Internet 3: Facebook") a) There are three assumptions : Linearity, Normality, Constant variance. Use plots in the next page to determine whether each assumption is met or not. Specify which plot you are using for each assumption. Check Canvas Study guide/summary table module and look for "Regression assumptions" document if you are not sure which plot to use. b) State the null and alternative hypothesis (again). c) Use a: = 0.05. Based on the R output below, report the value of test statistic and pvalue. Draw a conclusion and interpret in context of the problem. d) It is known that 95% CI 013 is bi(t0.025f:3o](SE) : 0.4389:|:(2.04)(0.1030) : (0.228, 0.649). Interpret the result in context. > summary (1m ( Facebook . Penetrat ion\"Internet .Penetrat. 1011)) Coefficients: Estimate Std. Error t value Pr(>|tl) (Intercept) 7.8980 5.5015 1.215 0.233925 Internet.Penetration 0.4389 0.1030 4.261 0.000185 **x Signif. codes: 0 %**'0.001'**'0.01'*'0.05'.'O.1' '1 Residual standard error: 12.84 on 30 degrees of freedom Multiple R-squared: 0.3771,:1djusted R-squared: 0.3553 /