Solutions

Please note that the steps show rounded numbers, but that the final answers to the problems are calculated without rounding.

Problem Part Solution
1 - chart
2 - \(\beta_0\) is the parameter y-intercept for the population
\(\beta_1\) is the parameter slope for the population.
\(\epsilon\) is the error term–a normal random variable.
3 A There is a linear relationship between X and Y. - Yes points on the scatter plot are close together and in a ‘hotdog’ shape.
scatter
3 B The error term \(\epsilon\) is normally distributed - Yes. Made a QQ plot of the residuals and the points are close to linear.
qq
3 C The variance of the error terms is constant for all values of X - Yes there is no megaphone shape in the residual scatter plot.
error
3 D X’s are fixed and measured without error. (In other words, the X’s can be considered as known constants.) We will assume that X’s have been measured accurately and precisely.
3 E The observations are independent. - We will assume that the Y’s are independent.
4 A \(H_0: \beta_1 = 0\)
\(H_a: \beta_2 \neq 0\)
4 B \(\text{Let alpha} = 0.05\)
4 C It is a t-test statistic
\(t = 22.675\)
4 D \(\text{P-value} = 0.000000000000508 < 0.05\)
Therefore we reject the null hypothesis.
4 E We have sufficient evidence to suggest that there is a linear relationship between the head length and the body length of the Gharial crocodiles.
5 - The 95% confidence interval for the true slope of the regression line is (6.704, 8.096)