A study was performed aimed at trying to further understand what factors contrib

Question

A study was performed aimed at trying to further understand what factors contribute to the home size of a family in the United States. The following data was obtained from a random sample of 10 families:

House Size Example:

Y X1 X2 X3

FT^2 Income Size Year

16 32 2 4

17 36 2 8

26 55 3 7

24 47 4 0

22 38 4 2

21 60 3 10

32 66 6 8

18 44 3 8

30 70 5 2

20 50 3 6

Variables

Y = Home Square Footage (Hundreds of Square Feet)

X1 = annual income (thousands of dollars)

X2 = Family Size

X3 = combined years of formal education (beyond high school) for

DEPENDENT VARIABLE(S) Y = Home Sqr Feet

INDEPENDENT VARIABLE(S) X1 = annual income

Questions;

Questions1.

Find the Regression Model that includes all three independent variables(2pts).

2.Find the coefficient of determination and the correlation coefficient for the Regression Model found in question #1. Interpret the meaning of each in the context of the problem(5pts).

3.Find the p-value for each independent variable, interpret each p-value, and determine which independent variables should be removed from the Regression Model(10pts).

4.Find the new Regression Model based on your analysis from question #3(2pts).

5. Compare the r2-adjusted, p-value, and F-value for the two Regression Models found in question #1 and question #4.Did the regression model improve? Explain(7pts).

6. Interpret the Regression Coefficients for the Regression Model found in question #4(6pts).

7.Using the Regression Model found in question #4, predict the home size for a family of 4, income of $52,000, and 6 years of formal education(3pts).[NOTE: if you removed one or more of the variables from your Regression Model, only use data for the remaining variable(s).]

1. This is output of full model .

Y = 5.6567 *X1 + 0.01938* X2 - 0.1627* X3

Is your regression model .

2.Find the coefficient of determination and the correlation coefficient for the Regression Model found in question #1. Interpret the meaning of each in the context of the problem(5pts).

coefficient of determination = 0.9052

See coefficient of determination 0.9052 is very strong that s why we say the model explains 90% of the variability of the response data around its mean

correlation coefficient = 0.9514

there is 0.9514 relationship between respose variable and regressor variables .

3.Find the p-value for each independent variable, interpret each p-value, and determine which independent variables should be removed from the Regression Model(10pts).

>>>>

See above otput and there p-value of each independent variable only variable size have P-values is less than 0..05 so size varible is significant anf other are not significant .

4.Find the new Regression Model based on your analysis from question #3(2pts).

After delating not significant variable new model

PLesae Answer the Questions 5,6 and 7 only

Regression Statistics MultipleR R Square Adjusted R Square Standard Error Observations 0.951454184 0.905265064 0.857897596 2.035454381 10 ANOVA MS Significance F Regression Residual Total 237.541552879.1805176 19.1115359 0.001792476 24.85844721 4.143074536 9 262.4 Coefficients Standard Error P-value Lower 95% U er 95% Lower 95.0% Upper 95.0% 1.27833 12.591764 0.08769957 2.210710561 0.069075670.020714752 0.40847148-0.0207148 0.40847148 0.907790908 2.575602317 0.04201717 0.116824035 4.5593927 0.11682404 4.5593927 0.244071095-0.666898793 0.52963317 -0.759991173 0.43444974-0.7599912 0.43444974 t Stat Intercept Income Size Year 5.656717014 0.193878366 2.338108367 0.162770718 2.834203853 1.995875141 0.09295612-1.278329981 12.591764

Explanation / Answer

5.
From part (1)

R^2-adjusted = 0.8578975 =85.78% of variation in the home square footage is explained by the independent variables home size, annual income , family sie and education

P-vaue of Regression 0.00179 < alpha 0.05, so we reject H0
Thus we conclude that the regression line is best fit to the given data

F - value = 19.1115359

From part (4)
R^2-adjusted = 0.82422 = 82.422% of variation in the home square footage is explained by the independent variables home size

P-vaue of Regression 0.000282 < alpha 0.05, so we reject H0
Thus we conclude that the regression line is best fit to the given data

Compart part(1) and Part(4)
The regression model is not improved in part (4) compare to part(1)

6. The p-value of size = 0.000282< alpha 0.05, so we reject H0
Thus the population regression coeffient of size is effected on the regression line

7. The predicted home square footage is
Y = 9.082759 + 3.862069 (4) = 24.531035

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