Chapter 27, Problem 1E

a)

To determine

To explain the about the regression.

Explanation of Solution

Given:

  

  

The regression equation is,

  $72Error=453.223-8.37084(YearSince1970)$

On average, the error made when predicting the path of the hurricanes is 453.223 nautical miles in the year 1970. The error made when predicting the path of the hurricanes decreases on average by 8.37084 nautical miles per year.

b)

To determine

To state the hypotheses about the slope.

Answer to Problem 1E

  $\begin{array}{l}{H}_0:{\beta }_1=0\\ H_a:{\beta }_1\ne 0\end{array}$

Explanation of Solution

Given:

  

  

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:{\beta }_1=0\\ H_a:{\beta }_1\ne 0\end{array}$

c)

To determine

To perform the hypothesis test.

Answer to Problem 1E

There is sufficient evidence that the prediction error change over the years.

Explanation of Solution

Given:

  

  

Formula:

Test statistic:

  $t=\frac{b-{\beta }_0}{S{E}_b}$

The null and alternative hypotheses:

  $\begin{array}{l}{H}_0:{\beta }_1=0\\ H_a:{\beta }_1\ne 0\end{array}$

Test statistic:

  $t=\frac{-8.37084-0}{1.209}=-6.9238$

The degrees of freedom = df = 34

Therefore, p-value would be,

P-value = 0 …Using excel formula, =TDIST(6.9238,34,2)

Decision: P-value < 0.05, reject H₀.

Conclusion: There is sufficient evidence that the prediction error change over the years.

d)

To determine

To explain R-square.

Answer to Problem 1E

The 58.5% of the variation between Years since 1970 and 72 Error has been explained by the regression model.

Explanation of Solution

Given:

  

  

  $R^2=58.5\%$

Therefore, 58.5% of the variation between Years since 1970 and 72 Error has been explained by the regression model.