Question

1.The scatterplot shows the weight (in pounds) and cost (in dollars) of 11 stand mixers. The mixer from Walmart (highlighted in red) was much lighter—and cheaper-than the other

Complete the following statement about the influence the highlighted point has on the standard deviation of the residuals and r^
Because the mixer from Walmart is a little closer to the least-squares regression line than the rest of the points in the data set, this mixer zéro will_________
1. significantly decrease
2. significantly increase
3. slightly increase
4. slightly decrease

the standard deviation of the residuals. The value of r^ ________
A) will decrease significantly
B) may decrease slightly
C) will increase significantly

Answer 1

The provided information suggests that the mixer from Walmart is closer to the least-squares regression line than the other points in the data set. Based on this, the statement about the influence on the standard deviation of the residuals and the coefficient of determination (r2 ) can be completed as follows:

1. Standard Deviation of the Residuals:

• Because the mixer from Walmart is closer to the least-squares regression line, it is likely to slightly decrease the standard deviation of the residuals. When a data point is closer to the regression line, the residuals (the vertical distances between the actual points and the regression line) tend to be smaller, contributing to a lower standard deviation of the residuals.

2. Coefficient of Determination (r2 ):

• The value of r2 will increase significantly. The coefficient of determination(r2) represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). When a point is closer to the regression line, it indicates that the linear model can explain a larger proportion of the variance in the dependent variable. Therefore, r2 will increase significantly.

So, the completed statement is:

• The mixer from Walmart will slightly decrease the standard deviation of the residuals, and the value of r2 will increase significantly.

Therefore, the correct choices are:

• For the standard deviation of the residuals: 4. slightly decrease
• For the value of r2: C) will increase significantly

Explanation: