MAT3024 Research Assignment on Regression Analysis
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Assignment Details:-
- Course Code: MAT3024
- Course Title: Regression Analysis
- Referencing Styles: Open
- Words: 1500
- University: Sunway University
- Country: MY
Assignment Task:-
A social researcher is interested in the relationship between income and happiness. A survey involving 498 people whose income ranges from $15k to $75k, and ranking of their happiness on a scale from 1 to 10, has been collected. The average income is $44,669.02.A simple linear regression model has been fitted to the dataset. School of Mathematical SciencesMAT3024/ August 2020Page 1of 12Question 1 A social researcher is interested in the relationship between income and happiness. A survey involving 498 people whose income ranges from $15k to $75k, and ranking of their happiness on a scale from 1 to 10, has been collected. The average income is $44,669.02.A simple linear regression model has been fitted to the dataset. The results of the regression analysis (income in $’000) are shown below.
(a)Identify the dependent variable and independent variables in this case.
(b)State the fitted model.
(c)Perform a hypothesis testing to see if there is a linear relationship between income and happiness.
(d)Find a 95% CI on the mean happiness if the income is $45k and the sum of squares of axis 150044.4.
(e)Suppose we wish to predict the happiness of a person given that his income is $45k. Give a point estimate of happiness. Find a 95% prediction interval on the happiness.
(f) Compare and explain the difference between the two intervals obtained in parts (d) and (e).