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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
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response explanatory Regression equation __________ on the y-axis
R-squared ___________ on the x-axis explanatory
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From Lecture 05:
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From Lecture 06: A residual is the vertical distance from a point to the regression line.
= observed - predicted
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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.
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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.
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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
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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
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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:
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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.)
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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
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