Exam 1

1. Question

   Using the data provided in regression.csv estimate a linear regression of y on x1 and x2. Answer the following questions.

   
   
   1. Proportion of variance explained (in percent):
   2. F-statistic:
   3. Characterize in your own words how the response y depends on the regressors x1 and x2.
   4. 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.

   
   
   1. Proportion of variance explained: 65.11 percent.
   2. F-statistic: 54.12.
   3. Characterization: semi-logarithmic.
   4. R code.