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
   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.