Model Multiple Regression Mathematics & Economics Math Problem

ASSIGNMENT 8
1 Suppose you fit the multiple regression model
y = β0 + β1x1 + β2x2 + ϵ
to n = 30 data points and obtain the following result: y=3.4-4.6x1+2.7x2+0.93x3
The estimated standard errors of β2 and β3 are 1.86 and .29, respectively.
* Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Ha: β2 ≠0. Use α = .05.
T= 2.71.86=1.45
We failed to reject the null hypothesis.
* Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Ha: β3 ≠0. Use α = .05.
T= 0.93.29=3.20
The null hypothesis is rejected.
* The null hypothesis H0: β2 = 0 is not rejected. In contrast, the null hypothesis H0: β3 = 0 is rejected. Explain how this can happen even though β2 > β3.
While the β2 > β3 happened because the values in the T distribution is greater than the former than the latter.
2 Use SPSS to fit a second-order model to the following data:
x

0

1

2

3

4

5

6

y

1

2.7

3.8

4.5

5.0

5.3

5.2

1 Find SSE and s2.
X Value

Error (Err) = (µ-X)

Error Squared (Err²)

1

-2.92857

8.57652

2.7

-1.22857

1.50938

3.8

-0.12857

0.01653

4.5

0.57143

0.32653

5.0

1.07143

1.14796

5.3

1.37143

1.88082

5.2

1.27143

1.61653

Sum of Squared Error (SSE) =

15.07427

S2

2.51

2 Do the data provide sufficient evidence to indicate that the second-order term provides information for the prediction of y? [Hint: Test H0: β2 = 0].
The data provided sufficient evidence to indicate that the second-order term can provide information to predict Y. The β2 = 0 which we reject the null hypothesis.
3 State the least squares prediction equation.
y = 0.6786x + 1.893
3 Running a manufacturing operation efficiently requires knowledge of the time it takes employees to manufacture the product, otherwise the cost of making the product cannot be determined. Estimates of production time are frequently obtained using time studies. The data in the table below came from a recent time study of a sample of 15 employees performing a particular task on an automobile assembly line.
Time to Assemble, y (minutes)

Months of Experience, x

10

24

20

1

15

10

11

15

11

17

19

3

11

20

13

9

17

3

18

1

16

7

16

9

17

7

18

5

10

20

4 Run the multiple linear regression model in SPSS. State the least squares prediction equation.
Regression Equation = ŷ = bX + a
b = SP/SSX = -344.8/774.93 = -0.44494
a = MY - bMX = 14.8 - (-0.44*10.07) = 19.27908
ŷ = -0.44494X + 19.27908
5 Test the null hypothesis H0: β2 =...