Lecture 5 MLR.2 Page 1 PDF

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These are lecture notes for Lecture 5 in Week 6 about Multiple Linear Regression Section 1....

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Lecture 5: MLR.2 Saturday, 20 February 2021

00:55

Chapter 6,7,8 (no 6.4, 7.4c, 7.5) This chapter brings together several issues with multiple regression analysis. • Specific types of variables • We have assumed that all x variables are continuous in nature, but now we try to explore what happens if x1 is a binary variable. How does the interpretation changes due to thus • The hypothesis testing and intuition doesn’t change, only the interpretation changes

6.1 Effects of Data Scaling on OLS Statistics •

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we briefly discussed the effects of changing the units of measurement on the OLS intercept and slope estimates. We also showed that changing the units of measurement did not affect R-squared. now return to the issue of data scaling and examine the effects of rescaling the dependent or independent variables on standard errors, t statistics, F statistics, and confidence intervals. When variables are rescaled, the coefficients, standard errors, confidence intervals, t statistics, and F statistics change in ways that preserve all measured effects and testing outcomes changing the dependent variable from ounces to pounds has no effect on how statistically important the independent variables are.

For Beta coefficients we want to ask what happens when the test score is one standard deviation higher. It is useful to obtain results when all variables have been standardized. A variable is standardised in the sample by subtracting off its mean and dividing by its standard deviation. (Computing Z-score)

6.2 More on Functional Form •

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Log showcases the semi elasticity of y variable with respect to control of other x variables. It shows that 1% increase in x variable effects the y variable. Using natural logs leads to coefficients with appealing interpretations, and we can be ignorant about the units of measurement of variables appearing in logarithmic form because the slope coefficients are invariant to rescaling....