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, x= percentage of Internet users and conduct a hypothesis test for H0 : = 0 against Ha : = 0. (The complete data set is available at https://istats.shinyapps.io/LinearRegression/ - Under Choose data set, click "Internet & 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. b) State the null and alternative hypothesis (again). c) Use = 0.05. Based on the R output below, report the value of test statistic and p-value.

Draw a conclusion and interpret in context of the problem. d) It is known that 95% CI for is b(t0.025,df=30)(SE) = 0.4389(2.04)(0.1030) = (0.228,0.649). Interpret the result in context. > summary(lm(Facebook.Penetration~Internet.Penetration)) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 7.8980 6.5015 1.215 0.233925 Internet.Penetration 0.4389 0.1030 4.261 0.000185 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 12.84 on 30 degrees of freedom Multiple R-squared: 0.3771,Adjusted R-squared: 0.3563