# Regression analysis - mean

1. Given the following data set:

X Y XY X2

2 6.1 12.2 4

3 7.3 21.9 9

5 10.4 52 25

5 9.4 47 25

6 10.7 64.2 36

7 12.1 84.7 49

28.0 56.0 282.0 148.0

™

ANOVA TABLE

Source Sum of Squares df Mean Square

Regression 24.641 1 24.641

Error .06123 4 .0153

Total 25 5

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a. Calculate X:

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b. Calculate Y:

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c. Calculate the Slope: B = ΣXY− n(X )(Y )/∑ X2 - n(X)2

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d. Calculate the Y-intercept: A = Y −B(X)

e. Write the regression equation; YC = A + B(X):

f. Predict YC for X =15:

g. Calculate the coefficient of determination:

h. Should you assume a significant relationship between the dependent and independent variables based on a 5% significance level?

You have been asked to support analysis of acquisition decisions involving net present value analysis.

1. You are analyzing the net present value of a project over a 16 year period. Based on the rates in the textbook, what is the actual discount rate you would use given that your analysis must consider the effects of inflation/deflation?

2. What is the present value of $25,000 that you will receive at the end of two years?

3. What is the present value of $2,000 a month over the next 3 years?

4. Cash Flow Scenario: Lease. Annual payments of $50,000 paid at the beginning of each of the next five years (total of $250,000). What is the NPV of all lease payments?

5. What is the net present value of a lease that requires you to pay $10,000 at the beginning of each year for the next five years and includes a provision for a rebate of $5,000 at eh end of Year 5?

6. What is the net present value of an item that has a purchase price of $20,000, requires $1,000 maintenance at the end of each year except year 4, and is expected to have a salvage valueof $1,000 at the end of the 5 year useful life?

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#### Solution Preview

1. Given the following data set:

From the attached EXCEL file we got the following:

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a. Calculate X: 4.67

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b. Calculate Y: 9.33

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c. Calculate the Slope: B = ΣXY− n(X )(Y )/∑ X2 - n(X)2 = Sxy/Sxx= 20.67/ 17.33 = 1.19

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d. Calculate the Y-intercept: A = Y −B(X) = 9.33 - 1.19(4.67) = 3.77

e. Write the regression equation; YC = A + B(X): Y= 3.77+1.19 X

f. Predict YC for X =15: Y(15) = 3.77+1.19(15) = 21.62

g. Calculate the coefficient of determination: R2=0.98

h. Should you assume a significant relationship between the dependent and independent variables based on a 5% significance level?

Since ...

#### Solution Summary

Determining the simple linear regression line.