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It is given in the question that,

According to the table, the heights of husbands and wives are correlated as:$r=0.5$

In regression analysis, the least-squares line is:

$\stackrel{鈭�}{Y}=a+bX$with slope $\stackrel{鈭�}{Y}=a+bX$and$Y$intercept $a$= $\stackrel{-}{Y}-b\stackrel{-}{X}$

Based on the least-squares regression line plotting husband's height against wife's height, the slope is as follows:

localid="1649943536880" $$\begin{gathered} b=0.5脳\frac{2.7}{2.5} \\ =0.54 \end{gathered}$$

Since the least-squares line passes through$\left(\stackrel{-}{X,}\stackrel{-}{Y}\right)$we use this information to find the intercept.

localid="1649943542257" $$\begin{gathered} \stackrel{-}{Y}=a+b\stackrel{-}{X} \\ a=68.5-0.54脳64.5 \\ =33.67 \end{gathered}$$

It is given in the question that, The correlation between the heights of husbands and wives is about r = $0.5$.

Use your regression line to predict the height of the husband of a woman who is $67$inches tall.

Based on a woman who stands$67$inches tall, the height of her husband is,

localid="1650003095350" $$\begin{gathered} \stackrel{鈭�}{Y}=33.67+0.54X \\ =33.67+0.54脳67 \\ =69.85 \end{gathered}$$

$\stackrel{鈭�}{Y}=69.85inches$

For a specific value of the explanatory variable localid="1649943566363" $X$, a regression line is used to predict the responselocalid="1649943572450" $Y$.