1. Lecture #26 Thursday, November 17, 2016 Textbook: 14.1 and 14.3
Statistics 200
Lecture #26 Thursday, November 17, 2016
Textbook: and 14.3
Objectives:
• Calculate T-statistic for test of the slope parameter in a regression problem
• Distinguish between deviation and residual
• Express r2 in terms of sums of squares

2. response explanatory Regression equation __________ on the y-axis
R-squared
___________ on the x-axis
explanatory

3. From Lecture 05:

4. From Lecture 06: A residual is the vertical distance from a point to the regression line.
= observed - predicted

5. Population version of regression (ith individual)
The value εi is called the deviation. We assume that it is normal with mean 0 and standard deviation σ.
Sample version of regression (ith individual)
The value ei is called the residual. The standard deviation of all the ei can be used to estimate σ.

6. From Lecture 06: Squared correlation
The squared value for the correlation (r2) is often used to describe the strength of the linear relationship.
Since the r2 value is simply r squared, the possible values for r2 range from 0 to 1.
Interpretation: quantifies the amount of variation in the response variable that can be attributed to the linear relationship with the explanatory variable.

7. Why does r2 give the proportion of variation explained?
SSE (sum of squared errors):
Add up all of the
(yi – y-hat)2 values
SSTO (total sum of squares):
Add up all of the
(yi – y-bar)2 values

8. Why does r2 give the proportion of variation explained?
SSE (sum of squared errors):
Add up all of the
(yi – y-hat)2 values
SSTO (total sum of squares):
Add up all of the
(yi – y-bar)2 values

9. The Test Statistic for H0: β1=0
For the hypothesis tests for slope, the __________ is used.
The t-statistic is calculated in the same way as before:

10. Example: Age and Reading Distance
The t-statistic is calculated like this:
The Minitab output would look like this:
Handy formula for the t-statistic:
(in this dataset, n=30.)

11. If you understand today’s lecture…
14.11, 14.12, 14.13, 14.15, 14.16
Objectives:
• Calculate T-statistic for test of the slope parameter in a regression problem
• Distinguish between deviation and residual
• Express r2 in terms of sums of squares