Question

QUESTION BLOCK: Linear Regression and R-squared

If we know the value of b, the slope of the regression line, we can accurately guess the value for the correlation coefficient without looking at the scatterplot.

1. True
2. False

For a biology project, you measure the weight in grams, and the tail length, in millimeters (mm), of a group of mice. The equation of the least-squares line for predicting tail length from weight is

predicted tail length = 20 +3*weight

Suppose a mouse weighing 20 grams has a 78 mm tail. What is the residual for this mouse?​​​​​​​

1. -2mm
2. 80mm
3. 2mm
4. 0mm

Which of the following makes NO distinction between an explanatory variable X and a response variable Y (i.e. you can interchange the roles of X and Y and get the same result)?​​​​​​​

1. Correlation
2. Regression
3. Both correlation and regression make no distinction between X and Y.
4. Both correlation and regression make distinction between X and Y.

The mean height of American women in their twenties is about 64 inches, and the standard deviation is about 2.7 inches. The mean height of men the same age is about 69.3 inches, with standard deviation about 2.8 inches. If the correlation between the heights of husbands and wives is about r = 0.5, what is the slope of the regression line used to predict the husband’s height (Y) from the wife’s height (X) in young couples?

Note: b = r(sy/sx)​​​​​​​

1. 1.0191
2. 0.4821
3. 0.5185
4. 1.0370

The correlation coefficient r has the same unit of measurement as the response variable:

1. True
2. False

Answer 1

If we know the value of b, the slope of the regression line, we can accurately guess the value for the correlation coefficient without looking at the scatterplot. FALSE

Predicted tail length = 20 +3*weight

Predicted tail length for weight = 20 grams is: 20 +3*20 = 80 mm

Actual tail length = 78 mm

Residual = Actual - Predicted = 78 - 80

Residual = -2 mm

Correlation makes NO distinction between an explanatory variable X and a response variable Y

Given, sx = 2.8, sy = 2.7 and r = 0.5

Slope b = r(sy/sx) = 0.5*(2.7/2.8)

Slope b = 0.4821

The correlation coefficient r has the same unit of measurement as the response variable FALSE