# Finally, the researcher considers using regression analysis to establish a linear relationship between the two variables – hours worked per week and yearly income. Hours per week   Yearly Income ('000's)   18 43.8p 13 44.5 18 44.8 25.5 46.0 11.5 41.2 18 43.3 16 43.6 27 46.2 27.5 46.8 30.5 48.2 24.5 49.3 32.5 53.8 25 53.9 23.5 54.2 30.5 50.5 27.5 51.2 28 51.5 26 52.6 25.5 52.8 26.5 52.9 33 49.5 15 49.8 27.5 50.3 36 54.3 27 55.1 34.5 55.3 39 61.7 37 62.3 31.5 63.4 37 63.7 24.5 55.5 28 55.6 19 55.7 38.5 58.2 37.5 58.3 18.5 58.4 32 59.2 35 59.3 36 59.4 39 60.5 24.5 56.7 26 57.8 38 63.8 44.5 64.2 34.5 55.8 34.5 56.2 40 64.3 41.5 64.5 34.5 64.7 42.3 66.1 34.5 72.3 28 73.2 38 74.2 31.5 68.5 36 69.7 37.5 71.2 22 66.3 33.5 66.5 37 66.7 43.5 74.8 20 62.0 35 57.3 24 55.3 20 56.1 41 61.5     a) What is the dependent variable and independent variable for this analysis? Why?  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. 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.  d) Display and interpret the value of the coefficient of determination, R-squared (R2).

Question

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

 Hours per week Yearly Income ('000's) 18 43.8p 13 44.5 18 44.8 25.5 46.0 11.5 41.2 18 43.3 16 43.6 27 46.2 27.5 46.8 30.5 48.2 24.5 49.3 32.5 53.8 25 53.9 23.5 54.2 30.5 50.5 27.5 51.2 28 51.5 26 52.6 25.5 52.8 26.5 52.9 33 49.5 15 49.8 27.5 50.3 36 54.3 27 55.1 34.5 55.3 39 61.7 37 62.3 31.5 63.4 37 63.7 24.5 55.5 28 55.6 19 55.7 38.5 58.2 37.5 58.3 18.5 58.4 32 59.2 35 59.3 36 59.4 39 60.5 24.5 56.7 26 57.8 38 63.8 44.5 64.2 34.5 55.8 34.5 56.2 40 64.3 41.5 64.5 34.5 64.7 42.3 66.1 34.5 72.3 28 73.2 38 74.2 31.5 68.5 36 69.7 37.5 71.2 22 66.3 33.5 66.5 37 66.7 43.5 74.8 20 62.0 35 57.3 24 55.3 20 56.1 41 61.5

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

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.

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.

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

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