Exam 1

1. Question

   Consider the following regression results:

   
   Call:
   lm(formula = y ~ x, data = d)
   
   Residuals:
        Min       1Q   Median       3Q      Max 
   -2.14867 -0.82868 -0.07472  0.66596  2.54119 
   
   Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
   (Intercept) 0.0001676  0.1254992   0.001    0.999    
   x           1.2492437  0.1241613  10.061 2.04e-14 ***
   ---
   Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
   
   Residual standard error: 0.9786 on 59 degrees of freedom
   Multiple R-squared:  0.6318,    Adjusted R-squared:  0.6255 
   F-statistic: 101.2 on 1 and 59 DF,  p-value: 2.043e-14

   Describe how the response y depends on the regressor x.

   
   

   Solution

   The presented results describe a linear regression.

   The mean of the response y increases with increasing x.

   If x increases by 1 unit then a change of y by about 1.25 units can be expected.

   Also, the effect of x is significant at the 5 percent level.