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).
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Finally, the researcher considers using
|
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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