Chapter 8, Problem 19E

(a)

To determine

To find out what is the correlation between size and price and explain why you chose the sign $(+\text{ or }-)$ you did.

Answer to Problem 19E

The correlation between size and price is $0.845$ .

Explanation of Solution

It is given in the question that, a random sample of records of sales of homes gives the price and size of homes. A regression to predict price from size has an R -squared of $\text{71}\text{.4\%}$ . The residual plot indicated that a linear model is appropriate. Thus, the correlation between size and price is calculated as:

  $\begin{array}{l}{r}^2=R^2\\ \Rightarrow r^2=0.714\\ \Rightarrow r=\sqrt{0.714}\\ \Rightarrow r=0.845\end{array}$

Thus, the correlation between size and price is $0.845$ . In this, we use the $+$ sign because larger homes cost more.

(b)

To determine

To explain what would you predict about the price of a home $1$ standard deviation above average in size.

Explanation of Solution

It is given in the question that, a random sample of records of sales of homes gives the price and size of homes. A regression to predict price from size has an R -squared of $\text{71}\text{.4\%}$ . The residual plot indicated that a linear model is appropriate. Thus, we predict about the price of a home $1$ standard deviation above average in size because price should be $0.845$ standard deviations above the mean in price.

(c)

To determine

To explain what would you predict about the price of a home $2$ standard deviation below average in size.

Explanation of Solution

It is given in the question that, a random sample of records of sales of homes gives the price and size of homes. A regression to predict price from size has an R -squared of $\text{71}\text{.4\%}$ . The residual plot indicated that a linear model is appropriate. Thus, we would you predict about the price of a home $2$ standard deviation below average in size because price should be $1.690$ standard deviations below the mean in price.