Suppose we run a regular multiple regression of a response variable y on 3 predictors, and find the following output. Estimate Std. Error t value Pr(>|t|) (Intercept) -0.7620 0.5268 -1.446 0.155 х1 x2 -5.3746 4.1160 -1.306 0.198 2.9286 2.5733 1.138 0.261 x3 2.9031 1.3875 2.092 0.042 * Signif. codes: 0**** 0.001 *** 0.01 ** 0.05 ' 0.1 '' 1 Residual standard error: 1.121 on 46 degrees of freedom Multiple R-squared: 0.1053, Adjusted R-squared: 0.04692 F-statistic: 1.804 on 3 and 46 DF, p-value: 0.1597 Suppose instead we decided to centre the response and predictors (centred at their mean, e.g. (y – y), (x1 – x1), etc.), and run the regression on these centred values. What would the value of the intercept be?
Suppose we run a regular multiple regression of a response variable y on 3 predictors, and find the following output. Estimate Std. Error t value Pr(>|t|) (Intercept) -0.7620 0.5268 -1.446 0.155 х1 x2 -5.3746 4.1160 -1.306 0.198 2.9286 2.5733 1.138 0.261 x3 2.9031 1.3875 2.092 0.042 * Signif. codes: 0**** 0.001 *** 0.01 ** 0.05 ' 0.1 '' 1 Residual standard error: 1.121 on 46 degrees of freedom Multiple R-squared: 0.1053, Adjusted R-squared: 0.04692 F-statistic: 1.804 on 3 and 46 DF, p-value: 0.1597 Suppose instead we decided to centre the response and predictors (centred at their mean, e.g. (y – y), (x1 – x1), etc.), and run the regression on these centred values. What would the value of the intercept be?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 6PPS
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Transcribed Image Text:Suppose we run a regular multiple regression of a response variable y on 3
predictors, and find the following output.
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.7620 0.5268 -1.446 0.155
х1
-5.3746 4.1160 -1.306 0.198
x2
2.9286 2.5733 1.138 0.261
x3
2.9031 1.3875 2.092 0.042*
Signif. codes: 0**** 0.001 ** 0.01 ** 0.05 ' 0.1 '' 1
Residual standard error: 1.121 on 46 degrees of freedom
Multiple R-squared: 0.1053, Adjusted R-squared: 0.04692
F-statistic: 1.804 on 3 and 46 DF, p-value: 0.1597
Suppose instead we decided to centre the response and predictors (centred at their
mean, e.g. (y – ỹ), (x1 – x1), etc.), and run the regression on these centred values.
What would the value of the intercept be?
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