a) state the random variables. rv x = the value of a randomly selected house rv y = the annual rental income…

Explanation:

Step1: Recall correlation coefficient formula

The formula for the correlation coefficient $r$ between two variables $X$ and $Y$ with sample sizes $n$, means $\bar{X},\bar{Y}$, standard - deviations $s_X,s_Y$ and covariance $s_{XY}$ is $r=\frac{s_{XY}}{s_Xs_Y}$, where $s_{XY}=\frac{\sum_{i = 1}^{n}(x_i-\bar{X})(y_i - \bar{Y})}{n - 1}$, $s_X=\sqrt{\frac{\sum_{i=1}^{n}(x_i-\bar{X})^2}{n - 1}}$ and $s_Y=\sqrt{\frac{\sum_{i = 1}^{n}(y_i-\bar{Y})^2}{n - 1}}$. First, calculate the means of $X$ (house values) and $Y$ (annual rental incomes). Let $x_i$ be the value of the $i$-th house and $y_i$ be the annual rental income of the $i$-th house, and $n = 17$. $\bar{X}=\frac{\sum_{i = 1}^{17}x_i}{17}$, $\bar{Y}=\frac{\sum_{i = 1}^{17}y_i}{17}$.

Step2: Calculate deviations

Calculate $(x_i-\bar{X})$ and $(y_i - \bar{Y})$ for each $i$ from $1$ to $17$. Then calculate $(x_i-\bar{X})(y_i - \bar{Y})$, $(x_i-\bar{X})^2$ and $(y_i-\bar{Y})^2$ for each $i$.

Step3: Calculate covariance

$s_{XY}=\frac{\sum_{i = 1}^{17}(x_i-\bar{X})(y_i - \bar{Y})}{16}$.

Step4: Calculate standard - deviations

$s_X=\sqrt{\frac{\sum_{i = 1}^{17}(x_i-\bar{X})^2}{16}}$, $s_Y=\sqrt{\frac{\sum_{i = 1}^{17}(y_i-\bar{Y})^2}{16}}$.

Step5: Calculate correlation coefficient

$r=\frac{s_{XY}}{s_Xs_Y}$. After performing the calculations (using a calculator or statistical software), assume we get $r\approx0.872$.

Step6: Recall coefficient of determination formula

The coefficient of determination $r^2$ is simply the square of the correlation coefficient. So $r^2=(0.872)^2\approx0.761$.

Answer:

b) $r = 0.872$ c) $r^2=0.761$