Question

This is true and false and if the asnwer is false i need the correct answer.

_____ The least squares slope for predicting y from x is the same asthe least squares slope for predicting xfrom y

_____ The least squares linepasses through the point of averages .

_____ A residual is the deviation of a point from the point of averages

_____ It is common to use a residual plotbased on plotting the residuals versus x.

______Theleast squares lineis the line that minimizes the sum of the squared deviations about the line.

_______Given    and r= .87. We can interpret r in context by saying “There is a strong, positive, linear causation between speed limit and average number of accidents per week.

The expected change in the value of  y for a one unit change in x is .

________ In the simple linear regression model, and are fixed numbers that are usually unknown.   

________ The slope b of the LSRL is an unbiasedestimator of the true slope .

________ Using the interceptfrom each LSRL a sampling distribution for the interceptof the true LSRL can be created

Answer 1

1. The least squares slope for predicting y from x is the same as the least squares slope for predicting x from y (False)

The relation between slope for predicting y from x i.e. and slope for predicting x from y is or where r is the correlation coefficient between x and y.

2. The least squares linepasses through the point of averages . (True)

3. A residual is the deviation of a point from the point of averages. (False)

A residual is the deviation of a point from its predicted value as given from the least sqaure equation.

4. It is common to use a residual plotbased on plotting the residuals versus x. (True)

5. The least squares line is the line that minimizes the sum of the squared deviations about the line. (True)

6. Given    and r= .87. We can interpret r in context by saying “There is a strong, positive, linear causation between speed limit and average number of accidents per week. (True)

7. The slope b of the LSRL is an unbiased estimator of the true slope (True)

8. Using the intercept from each LSRL a sampling distribution for the intercept of the true LSRL can be created. (True)