Question
Using the data provided in regression.csv estimate a linear regression of
y on x1 and x2. Answer the following questions.
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Proportion of variance explained (in percent):
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F-statistic:
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Characterize in your own words how the response y depends on the regressors x1 and x2.
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Upload the R script you used to analyze the data.
Solution
The presented results describe a semi-logarithmic regression.
Call:
lm(formula = log(y) ~ x1 + x2, data = d)
Residuals:
Min 1Q Median 3Q Max
-2.68802 -0.67816 -0.01803 0.68866 2.35064
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.06802 0.13491 -0.504 0.616
x1 1.37863 0.13351 10.326 9.34e-15
x2 -0.21449 0.13995 -1.533 0.131
Residual standard error: 1.052 on 58 degrees of freedom
Multiple R-squared: 0.6511, Adjusted R-squared: 0.6391
F-statistic: 54.12 on 2 and 58 DF, p-value: 5.472e-14
The mean of the response y increases with increasing x1.
If x1 increases by 1 unit then a change of y by about 296.94 percent can be expected.
Also, the effect of x1 is significant at the 5 percent level.
Variable x2 has no significant influence on the response at 5 percent level.
The R-squared is 0.6511 and thus 65.11 percent of the
variance of the response is explained by the regression.
The F-statistic is 54.12.
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Proportion of variance explained: 65.11 percent.
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F-statistic: 54.12.
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Characterization: semi-logarithmic.
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R code.