In: Statistics and Probability
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.
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?
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)?
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)
The correlation coefficient r has the same unit of measurement as the response variable:
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