Question
========
Using the data provided in [regression.csv](regression.csv) estimate a linear regression of
`y` on `x1` and `x2`. Answer the following questions.
Answerlist
----------
* Proportion of variance explained (in percent):
* F-statistic:
* Characterize in your own words how the response `y` depends on the regressors `x1` and `x2`.
* 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
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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.
Answerlist
----------
* Proportion of variance explained: 65.11 percent.
* F-statistic: 54.12.
* Characterization: semi-logarithmic.
* R code.
Meta-information
================
exname: Regression cloze essay
extype: cloze
exsolution: 65.11|54.12|nil|nil
exclozetype: num|num|essay|file
extol: 0.1