## A Complete Example

This section explains linear regression, from presenting the data to using scatter plots to identify the linear pattern. It then fits a linear model using least squares estimation and addresses statistical inferences on correlation coefficient and slope parameter.

### Answers

1.

, , , , .

, , .

, .

, .

.

.

, .

, .

The 95% confidence interval for is: .

At , the 95% confidence interval for is .

At , the 95% prediction interval for is .

3. The positively correlated trend seems less profound than that in each of the previous plots.

5. The regression line: . Coefficient of Correlation: . Coefficient of Determination: . . . A 95% confidence interval for . Test Statistic for . At , ; a 95% confidence interval for the mean value of is: ; and a 95% prediction interval for an individual value of is: .