Chapter PII, Problem 6RE

(a)

To determine

To find out what is the correlation between Dow index and Year.

Answer to Problem 6RE

  $r=0.9138$ .

Explanation of Solution

In the question, it is given that,

  $\begin{array}{l}\text{Constant}=-2294.01\\ \text{Year since 1970}=341.095\\ s=1577\\ R^2=83.5\%\end{array}$

Thus, the correlation between Dow index and Year is calculated as,

  $\begin{array}{l}{r}^2=R^2\\ \Rightarrow r^2=0.835\\ \Rightarrow r=\sqrt{0.835}\\ \Rightarrow r=0.9138\end{array}$

(b)

To determine

To write the regression equation.

Answer to Problem 6RE

   .

Explanation of Solution

In the question, it is given that,

  $\begin{array}{l}\text{Constant}=-2294.01\\ \text{Year since 1970}=341.095\\ s=1577\\ R^2=83.5\%\end{array}$

The regression line will be equated as,

  

(c)

To determine

To explain in this context what the equation says.

Explanation of Solution

In the question, it is given that,

  $\begin{array}{l}\text{Constant}=-2294.01\\ \text{Year since 1970}=341.095\\ s=1577\\ R^2=83.5\%\end{array}$

The regression line will be equated as,

  

Thus, from the equation we interpret that every year after $1970$ the Dow Index will increase by $341.095$ and the y -intercept is $-2294.01$ which would not make sense because the Dow Index would not be negative in value.

(d)

To determine

To explain which assumption of the regression analysis appear to be violated.

Explanation of Solution

In the question, it is given that,

  $\begin{array}{l}\text{Constant}=-2294.01\\ \text{Year since 1970}=341.095\\ s=1577\\ R^2=83.5\%\end{array}$

The regression line will be equated as,

  

Thus, we can say that the assumption of the regression analysis that appear to be violated is that the residual show that the scatterplot is not linear.