Question

Question 6 (10 marks) Finally, the researcher considers using regression analysis to establish a linear relationship between the two variables – hours worked per week and yearly income.

a) What is the dependent variable and independent variable for this analysis? Why? (2 marks)

b) Use an appropriate plot to investigate the relationship between the two variables. Display the plot. On the same plot, fit a linear trend line including the equation and the coefficient of determination R² . (2 marks)

c) Estimate a simple linear regression model and present the estimated linear equation. Display the regression summary table and interpret the intercept and slope coefficient estimates of the linear model. (4 marks)

d) Display and interpret the value of the coefficient of determination, R-squared (R² ). (2 marks)

Answer 1

Answer:-

Given That:-

Finally, the researcher considers using regression analysis to establish a linear relationship between the two variables – hours worked per week and yearly income.

a) What is the dependent variable and independent variable for this analysis? Why? (2 marks)

Given,

Here dependent variable is yearly income s independent variable is hours worked per week, because no. of hours a person can work is independent where as amount he earns depend on hours.

b) Use an appropriate plot to investigate the relationship between the two variables. Display the plot. On the same plot, fit a linear trend line including the equation and the coefficient of determination R2 . (2 marks)

As, data is not attached in the question , I have assumed following data-

Hours per week	Yearly Income
20	45000
12	44700
16	42500
25	54000
22	51000
15	49000
27	55000
37	62000

Scatter Plot-

Income (1,000) 100 90 80 To Trend line so 40 30 20 1o 5 10 15 20 25 30 35 yo 4J *(Mx)

Coefficient of determination = 0.9728

c) Estimate a simple linear regression model and present the estimated linear equation. Display the regression summary table and interpret the intercept and slope coefficient estimates of the linear model. (4 marks)

Lineat regression calcuator-

y = 779.27x + 32268

$\Sigma x=186$

$\Sigma y=703200$

$\bar{x}=23.25$

$\bar{y}=50400$

$ss_y=302200$

$\begin{pmatrix} b = sp/ss_x \\ a=M_y-bM_x \end{pmatrix}$

equation y = 779.87x + 32268

d) Display and interpret the value of the coefficient of determination, R-squared (R2 ). (2 marks)

The value of r2 = 0.9728, which means the given linear regression fits 97.28% of data.

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