Data: (Vixi1,.30 Call lm(formula = y ~ x1 + x2) Residuals: Min 1Q Median Max -1.6232 -0.6626 0.0234 0.4180 1.7137 Coefficients: Estimate Std. Error t value Pr(>t|) (Intercept) 5.59342.3223 2.409 0.0231* 0.3568 5.566 6.69e-06k* 0.4146 12.296 1.42e-12k* 1.9859 5.0974 Signif. codes: '*0.0010.01 '*" 0.05"." 0.1'1 Residual standard error: 0.8867 on 27 degrees of freedom Multiple R-squared e.8752, F-statistic: 94.64 on 2 and 27 DF, p-value: 6.322e-13 Analysis of Variance Table Adjusted R-squared: 0.8659 Response: y Df Sum Sq Mean Sq F value Pr(>F) 1 29.951 29.951 38.091 1.347e-06** 1 118.874 118.874 151.183 1.419e-12 Residuals 27 21.230 0.786 Signif. codes: e 0.001 0.01 State p - values/test statistics to 4 decimal places 0.05"." 0.1'1 a)Given the R output for the above model, test the following hypotheses stating the corresponding p-value and appropriate conclusion: p -value: Conclusion: There is sufficient evidence to reject Ho in favour of H1 thus we can conclude that there is a statistically significant relationship between y and x1 There is sufficient evidence to reject Ho in favour of H1 thus we can conclude that there is not a statistically significant relationship between y and x1 There is insufficient evidence to reject Ho in favour of Hi thus we can conclude that there is a statistically significant relationship between y andx There is insufficient evidence to reject Ho in favour of H1 thus we can conclude that there is not a statistically significant relationship between y and x1 ii) Ho,-2 vs. HH,#2 Test Statistic State the t-value you would compare your test statistic to for this hypothesis test: Conclusion: There is sufficient evidence to reject Ho in favour of H1 thus we can conclude that B1 is significantly different from 2 There is insufficient evidence to reject Ho in favour of H1 thus we can conclude that B1 is not significantly different from 2 There is insufficient evidence to reject Ho in favour of H1 thus we can conclude that B1 is significantly different from 2 b) Given (XTX)-1 below or otherwise, construct a 95% confidence interval for ! I,2] 1,3] [1,] 6.859102-0.445975969-1.079557001 [2,] -0.445976 0.161895369-9.009155426 [3,] -1.079557 -0.009155426 0.218577990 Give your answer to 2 decimal places Lower bound: Upper bound c) Construct a 95% prediction interval for a subject with the following measurements: X1-4 and X2 Give your answer to 2 decimal places Lower bound: 6. Data: (Vixi1,.30 Call lm(formula = y ~ x1 + x2) Residuals: Min 1Q Median Max -1.6232 -0.6626 0.0234 0.4180 1.7137 Coefficients: Estimate Std. Error t value Pr(>t|) (Intercept) 5.59342.3223 2.409 0.0231* 0.3568 5.566 6.69e-06k* 0.4146 12.296 1.42e-12k* 1.9859 5.0974 Signif. codes: '*0.0010.01 '*" 0.05"." 0.1'1 Residual standard error: 0.8867 on 27 degrees of freedom Multiple R-squared e.8752, F-statistic: 94.64 on 2 and 27 DF, p-value: 6.322e-13 Analysis of Variance Table Adjusted R-squared: 0.8659 Response: y Df Sum Sq Mean Sq F value Pr(>F) 1 29.951 29.951 38.091 1.347e-06** 1 118.874 118.874 151.183 1.419e-12 Residuals 27 21.230 0.786 Signif. codes: e 0.001 0.01 State p - values/test statistics to 4 decimal places 0.05"." 0.1'1 a)Given the R output for the above model, test the following hypotheses stating the corresponding p-value and appropriate conclusion: p -value: Conclusion: There is sufficient evidence to reject Ho in favour of H1 thus we can conclude that there is a statistically significant relationship between y and x1 There is sufficient evidence to reject Ho in favour of H1 thus we can conclude that there is not a statistically significant relationship between y and x1 There is insufficient evidence to reject Ho in favour of Hi thus we can conclude that there is a statistically significant relationship between y andx There is insufficient evidence to reject Ho in favour of H1 thus we can conclude that there is not a statistically significant relationship between y and x1 ii) Ho,-2 vs. HH,#2 Test Statistic State the t-value you would compare your test statistic to for this hypothesis test: Conclusion: There is sufficient evidence to reject Ho in favour of H1 thus we can conclude that B1 is significantly different from 2 There is insufficient evidence to reject Ho in favour of H1 thus we can conclude that B1 is not significantly different from 2 There is insufficient evidence to reject Ho in favour of H1 thus we can conclude that B1 is significantly different from 2 b) Given (XTX)-1 below or otherwise, construct a 95% confidence interval for ! I,2] 1,3] [1,] 6.859102-0.445975969-1.079557001 [2,] -0.445976 0.161895369-9.009155426 [3,] -1.079557 -0.009155426 0.218577990 Give your answer to 2 decimal places Lower bound: Upper bound c) Construct a 95% prediction interval for a subject with the following measurements: X1-4 and X2 Give your answer to 2 decimal places Lower bound: 6
