Answers

1.

\(Σx=14.2\), \(Σy=49.6\), \(Σxy=91.73\), \(Σx^2=26.3\), \(Σy^2=333.86\).

\(SS_{xx}=6.136\), \(SS_{xy}=21.298\), \(SS_{yy}=87.844\).

\( \overline x =1.42\), \( \overline y =4.96\).

\(\hat β_1=3.47\), \(\hat β_0=0.03\).

\(SSE=13.92\).

\(sε=1.32\).

\(r = 0.9174\), \(r^2 = 0.8416\).

\(df=8\), \(T = 6.518\).

The 95% confidence interval for \(β_1\) is: \((2.24,4.70)\).

At \(x_p=2\), the 95% confidence interval for \(E(y)\) is \((5.77,8.17)\).

At \(x_p=2\), the 95% prediction interval for \(y\) is \((3.73,10.21)\).

3. The positively correlated trend seems less profound than that in each of the previous plots.

5. The regression line: \(\hat y=3.3426x+138.7692\). Coefficient of Correlation: \(r = 0.9431\). Coefficient of Determination: \(r^2 = 0.8894\). \(SSE=283.2473\). \(s_e=1.9305\). A 95% confidence interval for \(β_1: (3-.0733,3.6120)\). Test Statistic for \(H_0:β_1=0: T = 24.7209\). At \(x_p=10\), \(\hat y=172.1956\); a 95% confidence interval for the mean value of \(y\) is: \((171.5577,172.8335)\); and a 95% prediction interval for an individual value of \(y\) is: \((168.2974,176.0938)\).