Question

Assessed Value	Heating Area	Age
184400	2000	3.42
177400	1710	11.50
175700	1450	8.33
185900	1760	0.00
179100	1930	7.42
170400	1200	32.00
175800	1550	16.00
185900	1930	2.00
178500	1590	1.75
179200	1500	2.75
186700	1900	0.00
179300	1390	0.00
174500	1540	12.58
183800	1890	2.75
176800	1590	7.17

Write-up a short summary in current APA format of the results. Be sure to include the resulting model (equation) for the relationship determined by the regression analysis. Your summary should also include a discussion regarding the statistical significance of each of the independent variables and an explanation of the results.

The proper steps in order for multiple regression are:

Global test

1. Each I.V. - identify the P-value of the highest non-sig variable and eliminate that variable.
2. Re-run the analysis to see if any more can be removed...and repeat until all I.V. are significant.
3. Assess for multicollinearity
4. Assess for autocorrelation & normal probability
5. Develop the regression equation.

*Please shoe excel formulas when applicable.

Answer 1

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Answer:

Multiple regression using Excel.

Step 1) First enter the given data set in excel columns.

Step 2) Then click on Data >>> Data Analysis >>>Regression >>>>OK

Step 3) Input Y Range: Select the data of column "Assessed Value"

Input X Range: Select all the data from "Heating Area and Age " columns.

Click on Lable

then Click on Ouput Range

Look the following Image

Then Click on OK, we get following result.

From the above output, let's write the multiple linear regression equation as

Assessed Value = 163775.1236 + 10.7252 *Heating Area - 284.2543 * Age

R² = R Square = 0.8265 = 82.65%

R² is called as coefficient of determination

It is a measure of how much variation explain in dependent variable by the fitted regression equation.

So here about 82.65% variation in Assessed Value is explain from the fitted line

See the P-value of overall mode = Significance F = 0.0000

That is at least one of the independent variable is important in the prediction of dependent variable

Now observe the significance of Heating Area and Age these two independent variable.

p-value corresponding to Heating Area is 0.0039 < 0.05

so we can say that at 5% level of significance the variable Heating Area is significance variable in the prediction of Assessed Value

p-value corresponding to Age  is 0.0053 < 0.05

so we can say that at 5% level of significance the variable Age is also the significance variable in the prediction of Assessed Value.

Let's interpret slope of each independent variables

If we change one unit in Heating Area and Age is held constant then the expected change in Assessed Value is equal to 10.7252 that is one unit change in Heating Area will expected increase in Assessed Value upto 10.7252

If we change one unit in Age and Heating Area is held constant then the expected change in Assessed Value is equal to -284.2543 that is if we increase Age by one year then it will expected decrease in Assessed Value upto -284.2543