Question

1. the number of calories and the fat content in grams are shown in the following scatterplot 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 regression - line. If an outlier is removed, the regression line may change.

Step2: Analyze the position of the outlier

The outlier (80, 12) is likely pulling the regression line in its direction. Since the original slope is 0.074, and the outlier is likely an influential point that is "dragging" the line down - ward (assuming a positive linear relationship in general from the scatter - plot), removing it will make the new line steeper.

Step3: Determine the new slope

When the outlier is removed, the new least - squares regression line will have a slope greater than the original slope. So the new slope > 0.074.

Answer:

C. Slope > 0.074