Question

1. 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 relationship between the variables may change.

Step2: Analyze the position of the outlier

The outlier (80,12) is likely pulling the regression line downwards relative to the other data points. When removed, the line will better fit the remaining data. Since the outlier was pulling the line down, removing it will make the line steeper.

Step3: Recall the slope of the original line

The original regression line is $\hat{y}=1.778 + 0.074x$, where the slope is 0.074. Removing the outlier will increase the slope.

Answer:

C. Slope > 0.074