Sarah wants to estimate the relationship between individual earnings in the labour market (earn) and years of education achieved (educ). She collects data from a sample of 122 individuals on their monthly salaries (Y), measured in rands, and education levels (X), measured in years of education.

Based on these data, she derives the following estimates:

∑XY=41421943.8
∑X2=15472
∑X=1242
∑Y=3401031

Question 1

The value for the slope parameter is ?

Question 2

.The value for the intercept parameter is ?

Question 3

If se(β2)=212.4477226, construct a 99% confidence interval for the parameter. Pr( ?. ≤β2≤ . )=99%

Question 4

If se(β1)=2392.463897, construct a 99% confidence interval for the parameter. Pr( ? ≤β1≤ ?. )=99%

Question 5

Under a simple interpretation of the above results, if an individual wishes to earn a monthly salary of R50 000, how many years of education should they aim to achieve?

Question 6
At significance level α=0.1 test whether β1 is equal to 3000 or whether it is larger than 3000.

Step 1: The null hypothesis is stated as...

A.
H1:β1>3000

B.
H0:β1=3000

C.
H1:β1<3000

D.
H0:β1≠3000

E.
None of the above.

Question 7

Step 1: The alternative hypothesis is stated as...

A. None of the above.

B. H1:β1>3000

C. H0:β1≠3000

D. H1:β1≥3000

E. H1:β1=3000

Question 8

Step 2. The t-test statistic is... {0.1|0.2}

Question 9

Step 3. The critical value is... ?

Question 10

Step 4. The calculated test statistic is greater than the critical value.

True

False

Question 11

Sarah estimates a value of the residual sum of squares at 1531.6864 and for the estimated sum of squares she finds a value of 1634.2568.

Calculate the value of r2.

Question 12

Step 5. Therefore, the null hypothesis isn't rejected.

True

False

Question 13

Based on the above results, choose the best conclusion below.

A. Based on the above results, it cannot be concluded that an individual with no education will earn at least a R3000 per month.

B. Based on the above results, it can be concluded that zero education is associated with a less than R3000 monthly earnings.

C. Based on the above results, it cannot be concluded that no education is associated with an income of less than R3000 per month.

D. No conclusions can be drawn from this analysis since regression results cannot be interpreted causally.

E. Based on the above results, it can be concluded that having no education is the same as having a little education in terms of the expected monthly salary.

Question 14

At significance level α=0.1 test whether β2 is equal to 3000 or whether it is less than 3000.

Step 1: The null hypothesis is stated as...

A.
None of the above.

B.
H0:β2=3000

C.
H1:β2<3000

D.
H1:β2>3000

E.
H0:β2≠3000

Question 15

Step 1: The alternative hypothesis is stated as...

A. None of the above.

B. H1:β2<3000

C. H1:β2=3000

D. H0:β2≠3000

E. H1:β2>3000

Question 16

Step 2. The t-test statistic is...  Blank 1. Fill in the blank, read surrounding text.

Question 17 .

Step 3. The critical value is...

Question 18

Step 4. The calculated test statistic is less than the critical value.

True

False

Question 19

Step 5. Therefore, the null hypothesis is rejected.

True

False

Question 20

Based on the above results, choose the best conclusion below.

A. Based on the above results, it cannot be concluded that for any individual an additional year of education will result in a R3000 per month increase in income, on average.

B. Based on the above results, it cannot be concluded that a one year increase in education is associated with a rise in income of less than R3000 per month, on average.

C. Based on the above results, it cannot be concluded that an additional year of education is associated with a rise in income of more than R3000 per month, on average.

D. No conclusions can be drawn from this analysis since regression results cannot be interpreted causally.

E. Based on the above results, it can be concluded that that an additional year of education is associated with a rise in income of at least R3000 per month, on average.

Question 21

How would you interpret the value estimated for r2?

A. The X variable is positively correlated with the Y variable.

B. About half of the variation in labour market earnings is explained by variation in educational attainment.

C. The X variable is positively and moderately correlated with the Y variable.

D. Around 20% of variation in Y is explained by variation in X.

E. There is a strong positive correlation between education and earnings.

I need assistance from question 4 to the last question.

Solution

Given :

Sample of 122 observations are taken from monthly salaries (Y) and education levels (X)

Slope is 2403.90

Intercept value is 3404.723

3. Given :

Standard error of beta 2 is 212.4477226

Confidence interval - 99% or 0.01

T critical value at 0.01 level of significance for degree of freedom 122-2=120 is 2.3578

confidence interval at 0.01 level of significance is 1903 and 2904.818

Question

Sarah wants to estimate the relationship between individual earnings in the labour market (earn) and years of education achieved (educ). She collects data from a sample of 122 individuals on their monthly salaries (Y), measured in rands, and education levels (X), measured in years of education.

Based on these data, she derives the following estimates:

∑XY=41421943.8
∑X2=15472
∑X=1242
∑Y=3401031

Question 1

The value for the slope parameter is ?

Question 2

.The value for the intercept parameter is ?

Question 3

If se(β2)=212.4477226, construct a 99% confidence interval for the parameter. Pr( ?. ≤β2≤ . )=99%

Question 4

If se(β1)=2392.463897, construct a 99% confidence interval for the parameter. Pr( ? ≤β1≤ ?. )=99%

Question 5

Under a simple interpretation of the above results, if an individual wishes to earn a monthly salary of R50 000, how many years of education should they aim to achieve?

Question 6
At significance level α=0.1 test whether β1 is equal to 3000 or whether it is larger than 3000.

Step 1: The null hypothesis is stated as...

A.
H1:β1>3000
B.
H0:β1=3000
C.
H1:β1<3000
D.
H0:β1≠3000
E.
None of the above.

Question 7

Step 1: The alternative hypothesis is stated as...

A. None of the above.
B. H1:β1>3000
C. H0:β1≠3000
D. H1:β1≥3000
E. H1:β1=3000

Question 8

Step 2. The t-test statistic is... {0.1|0.2}

Question 9

Step 3. The critical value is... ?

Question 10

Step 4. The calculated test statistic is greater than the critical value.

True

False

Question 11

Sarah estimates a value of the residual sum of squares at 1531.6864 and for the estimated sum of squares she finds a value of 1634.2568.

Calculate the value of r2.

Question 12

Step 5. Therefore, the null hypothesis isn't rejected.

True

False

Question 13

Based on the above results, choose the best conclusion below.

A. Based on the above results, it cannot be concluded that an individual with no education will earn at least a R3000 per month.
B. Based on the above results, it can be concluded that zero education is associated with a less than R3000 monthly earnings.
C. Based on the above results, it cannot be concluded that no education is associated with an income of less than R3000 per month.
D. No conclusions can be drawn from this analysis since regression results cannot be interpreted causally.
E. Based on the above results, it can be concluded that having no education is the same as having a little education in terms of the expected monthly salary.

Question 14

At significance level α=0.1 test whether β2 is equal to 3000 or whether it is less than 3000.

Step 1: The null hypothesis is stated as...

A.
None of the above.
B.
H0:β2=3000
C.
H1:β2<3000
D.
H1:β2>3000
E.
H0:β2≠3000

Question 15

Step 1: The alternative hypothesis is stated as...

A. None of the above.
B. H1:β2<3000
C. H1:β2=3000
D. H0:β2≠3000
E. H1:β2>3000

Question 16

Step 2. The t-test statistic is... Blank 1. Fill in the blank, read surrounding text.

Question 17 .

Step 3. The critical value is...

Question 18

Step 4. The calculated test statistic is less than the critical value.

True

False

Question 19

Step 5. Therefore, the null hypothesis is rejected.

True

False

Question 20

Based on the above results, choose the best conclusion below.

A. Based on the above results, it cannot be concluded that for any individual an additional year of education will result in a R3000 per month increase in income, on average.
B. Based on the above results, it cannot be concluded that a one year increase in education is associated with a rise in income of less than R3000 per month, on average.
C. Based on the above results, it cannot be concluded that an additional year of education is associated with a rise in income of more than R3000 per month, on average.
D. No conclusions can be drawn from this analysis since regression results cannot be interpreted causally.
E. Based on the above results, it can be concluded that that an additional year of education is associated with a rise in income of at least R3000 per month, on average.

Question 21

How would you interpret the value estimated for r2?

A. The X variable is positively correlated with the Y variable.
B. About half of the variation in labour market earnings is explained by variation in educational attainment.
C. The X variable is positively and moderately correlated with the Y variable.
D. Around 20% of variation in Y is explained by variation in X.
E. There is a strong positive correlation between education and earnings.