Questions: The following table shows the relationship between weight and calories burned per minute for five people. Weight (in pounds) Calories burned per minute ---------------------------------------------- 112 7.25 129 9.15 150 9.85 174 10.25 Mean 182 11.75 Standard Deviation 149.4 9.65 29.51 1.64 Weight is the explanatory variable and has a mean of 149.4 and a standard deviation of 29.51. Calories burned per minute is the response variable and has a mean of 9.65 and a standard deviation of 1.64. The correlation was found to be 0.944. Select the correct slope and y-intercept for the least squares line (answer choices are rounded to the hundredths places).

Solution Steps

To find the slope and y-intercept of the least squares line, we use the formulas for the slope ($b$) and y-intercept ($a$) of the regression line $y = a + bx$. The slope is calculated using the formula $b = r \times \frac{\text{std\_dev\_y}}{\text{std\_dev\_x}}$, where $r$ is the correlation coefficient, $\text{std\_dev\_y}$ is the standard deviation of the response variable, and $\text{std\_dev\_x}$ is the standard deviation of the explanatory variable. The y-intercept is calculated using the formula $a = \text{mean\_y} - b \times \text{mean\_x}$, where $\text{mean\_y}$ and $\text{mean\_x}$ are the means of the response and explanatory variables, respectively.

To find the slope ($b$) of the least squares line, we use the formula: $$b = r \times \frac{\text{std\_dev\_y}}{\text{std\_dev\_x}}$$ Substituting the given values: $$b = 0.944 \times \frac{1.64}{29.51} \approx 0.05246$$

The y-intercept ($a$) is calculated using the formula: $$a = \text{mean\_y} - b \times \text{mean\_x}$$ Substituting the calculated slope and given means: $$a = 9.65 - 0.05246 \times 149.4 \approx 1.812$$

Final Answer