Questions: Foot temperatures: Foot ulcers are a common problem for people with diabetes. Higher skin temperatures on the foot indicate an increased risk of ulcers. In a study performed at the Colorado School of Mines, skin temperatures on both feet were measured, in degrees Fahrenheit, for 8 diabetic patients. The results are presented in the following table. Use a TI-84 calculator to answer the following. Left Foot Right Foot --- --- 80 80 75 80 85 85 88 86 89 87 78 78 87 82 88 89 Send data to Excel Part: 0 / 4 Part 1 of 4 Compute the least-squares regression line for predicting the right foot temperature from the left foot temperature. Round the slope and y-intercept values to four decimal places. ŷ =

Foot temperatures: Foot ulcers are a common problem for people with diabetes. Higher skin temperatures on the foot indicate an increased risk of ulcers. In a study performed at the Colorado School of Mines, skin temperatures on both feet were measured, in degrees Fahrenheit, for 8 diabetic patients. The results are presented in the following table. Use a TI-84 calculator to answer the following.

Left Foot Right Foot
--- ---
80 80
75 80
85 85
88 86
89 87
78 78
87 82
88 89

Send data to Excel

Part: 0 / 4

Part 1 of 4

Compute the least-squares regression line for predicting the right foot temperature from the left foot temperature. Round the slope and y-intercept values to four decimal places.

ŷ =

Transcript text: Foot temperatures: Foot ulcers are a common problem for people with diabetes. Higher skin temperatures on the foot indicate an increased risk of ulcers. In a study performed at the Colorado School of Mines, skin temperatures on both feet were measured, in degrees Fahrenheit, for 8 diabetic patients. The results are presented in the following table. Use a TI-84 calculator to answer the following. \begin{tabular}{cc} \hline Left Foot & Right Foot \\ \hline 80 & 80 \\ 75 & 80 \\ 85 & 85 \\ 88 & 86 \\ 89 & 87 \\ 78 & 78 \\ 87 & 82 \\ 88 & 89 \\ \hline \end{tabular} Send data to Excel Part: $0 / 4$ Part 1 of 4 Compute the least-squares regression line for predicting the right foot temperature from the left foot temperature. Round the slope and $y$-intercept values to four decimal places. \[ \widehat{y}=\square \]

Solution

Solution Steps

Step 1: Calculating the Means

The mean of x ($ar{x}$) is 83.75, and the mean of y ($ar{y}$) is 83.375.

Step 2: Calculating the Slope (m) of the Regression Line

The slope (m) is calculated using the formula: $m = \frac{\sum (x_i - ar{x})(y_i - ar{y})}{\sum (x_i - ar{x})^2}$, which results in $m = 0.625$.

Step 3: Calculating the Y-intercept (b) of the Regression Line

The y-intercept (b) is calculated using the formula: $b = ar{y} - mar{x}$, which results in $b = 31.005$.

Step 4: Calculating the Correlation Coefficient (r)

The correlation coefficient (r) is calculated using the formula: $r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}$, which results in $r = 0.85$.