STATISTICS 200 Lecture 26 Textbook 14 1 and

STATISTICS 200 Lecture #26 Textbook: 14. 1 and 14. 3 Thursday, November 17, 2016 Objectives: • Calculate T-statistic for test of the slope parameter in a regression problem • Distinguish between deviation and residual • Express r 2 in terms of sums of squares

response on the y-axis _____ Regression equation R-squared explanatory ______ on the x-axis

From Lecture 05:

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

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.

From Lecture 06: Squared correlation 2 The squared value for the correlation (r ) is often used to describe the strength of the linear relationship. 2 Since the r value is simply r squared, the possible values for r 2 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.

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

The Test Statistic for H 0: β 1=0 t-statistic is • For the hypothesis tests for slope, the _____ used. • The t-statistic is calculated in the same way as before:

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. )

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 r 2 in terms of sums of squares