Question 01: solution
a) Interpret the regression coefficients:
Interpretation of constant/intercept: The estimate of the intercept is 0.2033. This
value implies that when labour force participation rate of women in 1968 is zero,
labour force participation rate of women in 1972 will be positive 0.2033
Interpretation of regression coefficient (B2): The estimated value of the regression
coefficient is 0.6560. The estimated value implies that when labour force participation
rate of women in 1968 increases by 1, labour force participation rate of women in
1972 would increase by approximately 0.6560 labour force.
b) Are the regression coefficients statistically significant at the 5% level.
P value: missing
c) Explain the value of r-squared.
R2= 0.397
d) Test the null hypothesis H0: B2=1 using the t-test at the 1% level of significance
T-test approach: H0: B2=1
1% level of significance
Criticat value: 2.567
T value: constant = 2.0829
Coefficient = 3.3452
Question 02: solution (Table 5.5)
a) Prepare a scatter plot with salary on the Y axis and spending on the X axis. Also
fit a regression line through the scatter plot.
b) Generate and discuss the
descriptive statistics of the
variables
c) Generate and discuss the correlations between the variables.
d) Estimate the regression of salary on spending and interpret the results.
Interpretation of intercept: The estimated value of the intercept term is12129.37. The
estimated value implies that when both the spending is equal to zero, the salary would be
12129.37 million.
Interpretation of regression coefficient: The estimated value of the regression coefficient is
3.307585. The estimated value implies that when spending increases by 1 dollor, salary
would increase by 3.307585 dollars.
Generate the ANOVA table and explain how it can be used.
e) Use the 95% confidence interval to test the null hypothesis that the slope
coefficient is equal to zero.
The lower limit of confidence interval is 2.681192 and the upper limit is 3.933978. As the
null hypothesis doest not lies within the confidence interval, we can reject the null hypothesis
at 95% confidence interval.
Moreover, the T statistic and the P value also indicate the null hypothesis H0: B2=0 can be
rejected at 5% level of significance.
f) Use the 99% confidence interval to test the null hypothesis that the slope
coefficient is equal to one.
Question 03: solution (Table 7.7)
Y = number of oil wells drilled
X2= price of the wellhead in the previous period
X3= domestic output
X4= GNP in dollars
X5= trend variable
a) Generate descriptive statistics and the pairwise correlations.
b) Estimate a multiple regression of Y on the X variables. Also interpret the
regression results in detail.
Interpretation of intercept (B1) The estimated value of the intercept term is -9.854598.
The estimated value implies that when the number of oil wells drilled X2= price of
the wellhead in the previous period X3= domestic output X4= GNP in dollars X5=
trend variable are equal to zero, number of oil wells drilled would be -9.854598.
Interpretation of regression coefficient (X2) The estimated value of the regression
coefficient is 2.701012. The estimated value implies that when price of the wellhead
in the previous period increases by 1 million, number of oil wells drilled would
increase by 2.701012.
Interpretation of regression coefficient (X3) The estimated value of the regression
coefficient is 3.059606. The estimated value implies that when domestic output
increases by 1, number of oil wells drilled would increase by 3.059606.
Interpretation of regression coefficient (X4) The estimated value of the regression
coefficient is -0.0160601. The estimated value implies that when GNP increases by 1,
number of oil wells drilled would increase by approximately -0.0160601 million
dollars
Interpretation of regression coefficient (X5) the estimated value of the regression
coefficient is -0.0227016. The estimated value implies that when trend variable input
increases by 1 million days, number of oil wells drilled would increase by
-0.0227016.
Test the overall significance of the regression model using the F-test.
The regression results indicate that the F-statistic is equal to 8.99 and its p-value is
0.001. numerater is 4 and denominator is 26.
5% level of significance: Therefore, we can conclude that the overall model is
statistically significant at the 5% level of significance as the F statistic 8.99 is greater
As the overall model is significant, all the independent variables collectively explain
the variation in the dependent variable.
c) Comment on the goodness of fit of the regression model. How would you explain
Adjusted r-squared.
The regression results indicate that the R2 value is 0.5804. The R2 value implies that
59.04% of the variation.. The adjusted R2 value iss lightly lower than R2 as expected
d) Use the residuals of the regression to examine the hypothesis that the error term
is normally distributed. Explain your answer.
The following results were generated form Shapiro wilk normality test.
The P value of the test is 0.10081which is greater than 0.05. Hence, we concluded that the
residual (error term) is normally distributed.
