1.42 4.11 4.22 12.28 9.16 28.62 7.92 24.82 9.59 29.82 Find estimates for the linear model yi N(0,0²). Bo+Bixi +Ei where ei ~ That is find Bo, B1, 6. Also perform a test of the null hypothesis Ho B₁ = 0 at level a = 0.01. 1

b) Suppose you are given the following information for an OLS regression: Σχι X; Y = 830102,T = 22,x=416.5, y = 86.65, x = 3919654, RSS = 130.6 i) Calculate the ordinary least square regression line. Calculate SE (a) and SE (B) Perform the hypothesis test such that Ho: a = -60 versus H₁: α = -60 Perform the hypothesis test such that Ho: P = 0.4 versus H₁: B = 0.4 In both cases use a significance of 5%. ii) iii) iv)

4. The following output from R presents the results from computing a linear model. In our data example we are interested to study the relationship between students' academic performance api00 with variable enroll which is the number of students in the school. Call: Im (formula = api00 enroll, data = d) Residuals: мin 10 Median 30 Маx -285.50 -112.55 -6.70 95.06 389.15 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 744.25141 15.93308 46.711 < 2e-16 *** enroll -0.19987 0.02985 -6.695 7.34e-11 *** --- Signif. codes: O ' *** ' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 135 on 398 degrees of freedom Multiple R-squared: 0.1012, Adjusted R-squared: F-statistic: 44.83 on 1 and 398 DF, p-value: 7.339e-11 0.09898

Consider the paired data: I 1.42 y 4.11 4.22 12.28 9.16 28.62 7.92 24.82 9.59 29.82 Eį Find estimates for the linear model y = Bo+812, +e, where ~ N(0,0²). That is find 3o. 31, à. Also perform a test of the null hypothesis Ho 3₁ = 0 at level a = 0.01.