Question

the number of calories and the fat content in grams are shown in the following scatter - plot for ten major brands of hot dogs. the equation of the least - squares regression line is $hat{y}=1.778 - 0.074x$. if the outlier at (80,12) is removed, and a new least squares regression line is calculated, which of the following must be true about the new slope? a) slope = 1.778 b) slope = 0.074 c) slope > 0.074 d) slope < 0.074 e) slope > 1.778

Explanation:

Step1: Understand the effect of an outlier

Outliers can affect the least - squares regression line. If an outlier is removed, the regression line may change.

Step2: Analyze the given outlier

The original regression line is $\hat{y}=1.778 - 0.074x$. The outlier $(80,12)$ affects the slope. Since the outlier is likely pulling the line in a certain direction, when removed, the relationship between the variables (calories and fat content) will be more in line with the general trend of the remaining data points. In this case, the negative slope will become less negative (i.e., increase in magnitude).

Answer:

C. Slope > 0.074