Positive Linear Relationship Assignment

Answers
Question 1
Our model in column 2 is;
Ln wi = β0 +β1 (Beauty) + β2 (IQ) + β3 (Height) +μi
E [Ln wi | x] = β0 +β1 (Beauty) + β2 (IQ) + β3 (Height)
E [Ln wi | x] = β0 +0.029 (Beauty) + 0.166 (IQ) + 0.047(Height)
β1 =0.029. It shows that log wage increases by 0.029 when beauty increases by one unit.
Β2 = 0.166. The estimate indicates that the log wage increases by 0.166 when the IQ increases
by a unit.
Β3 =0.047. The estimate shows that the log wage increases by 0.047 when the height increases
by a unit.
Question 2
Ho: β1 ≥ 0 vs.
H1: β1 < 0
β1 is the regression estimate of the independent variable beauty. Therefore, the null hypothesis
states that there is a positive linear relationship between beauty and the log of annual earnings.
The alternative hypothesis states that there is a negative linear relationship between beauty and
the log of annual earnings.
Question 3
The estimates β1 and β2 of in column 3 are;
β1= 0.028
β2 =0.070

It is true to claim that IQ has more than twice the effect on earnings as beauty. The estimate of
IQ is greater than the estimate of beauty. IQ has more than twice the effect on earnings as
beauty. In the model, we determine how IQ influences earnings holding the variable beauty
constant and also the influence of beauty on earnings holding the variable IQ constant.
Question 4
Conducting a t-test
Ho: β2 ≥ 0.17 vs.
H1: β2 < 0.17
The p-value is 0.065. At a 1% level of significance, we fail to reject the null hypothesis since
0.065 > 0.01. Therefore, there is no enough evidence to conclude that the estimate of IQ is less
than 0.17.
At a 10% level of significance, we shall reject the null hypothesis and accept the alternative
hypothesis. Therefore, there is enough evidence to conclude that the regression estimate of IQ is
less than 0.17. It is because the p-value is less than 0.1 (0.065 <0.1).
Question 5
Usually, R-squared increases when we increase another predictor variable in the regression
model. In the first column, we had two predictor variables (beauty and IQ). In the second
column, we have three predictor variables (beauty, IQ and height). The R-squared of column
three is thus greater than the R-squared of column 2 (0.113 < 0.121). However, R-squared
increases only If the added variable has some statistically significant effect on the model.
Question 6
Ho: β1 = 0 vs.
H1: β1≠ 0
P-value is 0.006, which is less than 0.05.