Monthly Household Spending ($) Annual Household Income ($) Household Size 4,016 54000 3 3,159 30000 2 5,100 32000 4 4,742 50000 5 1,864 31000 2 4,070 55000 2 2,731 37000 1 3,348 40000 2 4,764 66000 4 4,110 51000 3 4,208 25000 3 4,219 48000 4 2,477 27000 1 2,514 33000 2 4,214 65000 3 4,965 63000 4 4,412 42000 6 2,448 21000 2 2,995 44000 1 4,171 37000 5 5,678 62000 6 3,623 21000 3 5,301 55000 7 3,020 42000 2 4,828 41000 7 5,573 54000 6 2,583 30000 1 3,866 48000 2 3,586 34000 5 5,037 67000 4 3,605 50000 2 5,345 67000 5 5,370 55000 6 3,890 52000 2 4,705 62000 3 4,157 64000 2 3,579 22000 3 3,890 29000 4 2,972 39000 2 3,121 35000 1 4,183 39000 4 3,730 54000 3 4,127 23000 6 2,921 27000 2 4,603 26000 7 4,273 61000 2 3,067 30000 2 3,074 22000 4 4,820 46000 5 5,149 66000 4 Use Excel’s Data Analysis tool to conduct a multiple regression analysis with annual income and household size as independent variables. Choose confidence level at 95%. Using significance level α=0.05. (1’) Please copy and paste the regression analysis output below. Based on the multiple regression analysis output, write the estimated multiple regression equation. Show decimal places to the thousands (e.g. 3.456) (0.5’) Interpret regression coefficients b1 and b2. (1’) (1) Interpret the multiple coefficient of determination r-square. (0.5’) (2) Compare the r-square of the simple linear model (shown in the scatter plot in Question a) and the r-square of the multiple regression model, what does the differences in r-squares tell us? (0.5’) What does F-test for significance tell us? (0.5’) What does t-test for significance tell us? (0.5’) Can you tell from the 95% confidence intervals whether the two independent variables are statistically significant? Explain. (0.5’) If a household has 3 members, and has an annual income of $100,000, predict this household’s monthly spending. Show decimal places to the thousands (e.g. 3.456) (0.5’) Is there any multicollinearity problem in the above regression model? How do you know? (0.5’)

Monthly Household Spending ($) Annual Household Income ($) Household Size 4,016 54000 3 3,159 30000 2 5,100 32000 4 4,742 50000 5 1,864 31000 2 4,070 55000 2 2,731 37000 1 3,348 40000 2 4,764 66000 4 4,110 51000 3 4,208 25000 3 4,219 48000 4 2,477 27000 1 2,514 33000 2 4,214 65000 3 4,965 63000 4 4,412 42000 6 2,448 21000 2 2,995 44000 1 4,171 37000 5 5,678 62000 6 3,623 21000 3 5,301 55000 7 3,020 42000 2 4,828 41000 7 5,573 54000 6 2,583 30000 1 3,866 48000 2 3,586 34000 5 5,037 67000 4 3,605 50000 2 5,345 67000 5 5,370 55000 6 3,890 52000 2 4,705 62000 3 4,157 64000 2 3,579 22000 3 3,890 29000 4 2,972 39000 2 3,121 35000 1 4,183 39000 4 3,730 54000 3 4,127 23000 6 2,921 27000 2 4,603 26000 7 4,273 61000 2 3,067 30000 2 3,074 22000 4 4,820 46000 5 5,149 66000 4 Use Excel’s Data Analysis tool to conduct a multiple regression analysis with annual income and household size as independent variables. Choose confidence level at 95%. Using significance level α=0.05. (1’) Please copy and paste the regression analysis output below. Based on the multiple regression analysis output, write the estimated multiple regression equation. Show decimal places to the thousands (e.g. 3.456) (0.5’) Interpret regression coefficients b1 and b2. (1’) (1) Interpret the multiple coefficient of determination r-square. (0.5’) (2) Compare the r-square of the simple linear model (shown in the scatter plot in Question a) and the r-square of the multiple regression model, what does the differences in r-squares tell us? (0.5’) What does F-test for significance tell us? (0.5’) What does t-test for significance tell us? (0.5’) Can you tell from the 95% confidence intervals whether the two independent variables are statistically significant? Explain. (0.5’) If a household has 3 members, and has an annual income of $100,000, predict this household’s monthly spending. Show decimal places to the thousands (e.g. 3.456) (0.5’) Is there any multicollinearity problem in the above regression model? How do you know? (0.5’)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Question

Monthly Household Spending ($)	Annual Household Income ($)	Household Size
4,016	54000	3
3,159	30000	2
5,100	32000	4
4,742	50000	5
1,864	31000	2
4,070	55000	2
2,731	37000	1
3,348	40000	2
4,764	66000	4
4,110	51000	3
4,208	25000	3
4,219	48000	4
2,477	27000	1
2,514	33000	2
4,214	65000	3
4,965	63000	4
4,412	42000	6
2,448	21000	2
2,995	44000	1
4,171	37000	5
5,678	62000	6
3,623	21000	3
5,301	55000	7
3,020	42000	2
4,828	41000	7
5,573	54000	6
2,583	30000	1
3,866	48000	2
3,586	34000	5
5,037	67000	4
3,605	50000	2
5,345	67000	5
5,370	55000	6
3,890	52000	2
4,705	62000	3
4,157	64000	2
3,579	22000	3
3,890	29000	4
2,972	39000	2
3,121	35000	1
4,183	39000	4
3,730	54000	3
4,127	23000	6
2,921	27000	2
4,603	26000	7
4,273	61000	2
3,067	30000	2
3,074	22000	4
4,820	46000	5
5,149	66000	4

Use Excel’s Data Analysis tool to conduct a multiple regression analysis with annual income and household size as independent variables. Choose confidence level at 95%. Using significance level α=0.05. (1’)

Please copy and paste the regression analysis output below.

Based on the multiple regression analysis output, write the estimated multiple regression equation.

Show decimal places to the thousands (e.g. 3.456) (0.5’)

Interpret regression coefficients b₁ and b₂. (1’)

(1) Interpret the multiple coefficient of determination r-square. (0.5’)

(2) Compare the r-square of the simple linear model (shown in the scatter plot in Question a) and the r-square of the multiple regression model, what does the differences in r-squares tell us? (0.5’)