Question

The equation of the least squares regression line for the points on the scatterplot above is y= 1.3 + 0.73x. What is the residual for the point (4,7)?

Answer 1

To calculate the residual for the point (4,7) on the regression line y=1.3+0.73x, subtract the predicted y-value (4.22) from the actual y-value (7), resulting in a residual of 2.78.

Step-by-step explanation:

The equation of the least squares regression line for the points on the scatterplot is given by y = 1.3 + 0.73x. To find the residual for a specific point, such as (4,7), you first need to calculate the predicted y-value (ŷ) using the regression equation. For x = 4, the predicted y-value is:

ŷ = 1.3 + (0.73 × 4)

= 1.3 + 2.92

= 4.22

The residual is the actual y-value minus the predicted y-value. So, for the point (4,7), the residual would be:

Residual = y - ŷ = 7 - 4.22

= 2.78

Therefore, the residual for the point (4,7) is 2.78.