Question

T/F 1-6

1. A regression line obtained by the least squares method is the line that maximizes the slope of the regression line.

2. In a simple regression model, the square of the correlation between the response variable and the explanatory variable is equal to the coefficient of determination of the regression model.

3. If the spread of residuals increases as the response variable of a regression model increases, the assumption of homoscedasticity is met.

4. The mean of the residuals of a regression model is assumed to be zero.

5.For a given confidence level, a confidence interval for the mean Y is wider than a prediction interval for an individual Y.

6. In a simple regression model, as the standard error of regression increases, the width of a confidence interval for the response variable also increases.

7. Which of the following chart is most appropriate to examine whether or not the residuals are correlated? -

a residual plot

a line fit plot

a normal probability plot

a lagged residual plot

Answer 1

Answer(1): False

Explanation: A regression line obtained by the least squares method is the line that minimizes the error.

Answer(2): True

Explanation: the correlation between the response variable and the explanatory variable is r and the coefficient of determination of the regression model is r2, hence the given statement is true.

Answer(3): False

Explanation: If the spread of residuals increases as the response variable of a regression model increases, the variance of residual does not remain constant, that means the residuals are heteroscedastic and the assumption of homoscedasticity is not met.

Answer(4): True

Explanation: it is basic assumption of regression model that the mean of residuals of a regression model is zero.

Answer(5): False

Explanation: It is other way round. A prediction interval for an individual Y is wider than a confidence interval for the mean Y.

Answer(6): True

Explanation: The confidence interval for the response variable is directly proportional to the standard error of regression model, so the given statement is true.

Answer(7):

The most appropriate to examine whether or not the residuals are correlated is A residual plot

The correct option is A. a residual plot.