Question

Eliza plans on constructing a confidence interval for the slope of a regression line. She creates the residual plot shown to check the conditions for creating the interval. Which of the following conditions appear to be met based on the residual plot?

I.The true relationship between x
and y
is linear.
II.The standard deviation of y
is constant for different levels of x
.
III.The value of 0 is contained in the confidence interval.

Answer 1

Based on the given residual plot, we can determine which conditions for constructing a confidence interval are met.

Step-by-step explanation:

Based on the given information, we can determine which conditions are met by analyzing the residual plot:

I. The true relationship between x and y is linear: If the residuals are randomly scattered around zero with no discernible pattern, it suggests a linear relationship. If the plot shows a random distribution of residuals, then this condition is met.

II. The standard deviation of y is constant for different levels of x: The plot should show a consistent spread of residuals across the range of x values. If the spread of residuals remains relatively constant, then this condition is met.

III. The value of 0 is contained in the confidence interval: The confidence interval represents the range of plausible values for the slope of the regression line. If the interval includes the value of 0, it suggests that there might not be a significant relationship between x and y.