Basic statistics Homework Assignment #8 complete solutions correct answers key

Basic statistics Homework Assignment #8 complete solutions correct answers key

Please study Ch13 to finish this homework assignment. You can calculate the answers following steps in the textbook practice (Computing a and b for the prediction Equation on Page 424-427 and TESTING THE SIGNIFICANCE OF R² USING ANOVA on Page 441-445) and weekly materials in BlackBoard. Also, please familiar with how to interpret the results using your own words following each definitions (See interpretation on Page 427-429). Table 13.4 (P.426) provides a clear, sequential example of the steps to follow to calculate the regression coefficients. By following the steps in this table, you not only learn about the calculation of the regression coefficients, but also about the logic of how the regression equation is constructed. Of course, one additional caveat: continue to remind yourself about the issue of rounding error and should develop a general classroom rule to round to a specific decimal point (i.e., 2 decimal points) for all calculations.

Problem set 2: use the following information to answer questions 5-9 (40 points total):

Let’s examine the relationship between GNP per capita and the percentage of respondents willing to pay more in taxes.

1.      In this chapter, we used Table 13.4 to illustrate how to calculate the slope and intercept in the regression table. Using table 13.4 as a model, create a similar table using the data below for GNP per capita and the percentage willing to pay higher taxes (10 pts).

GNP per Capita (X)

% Willing to Pay Higher Taxes (Y)

(X -)

 (X -)²

(Y -)

(Y -) ²

(X -) (Y -)

19.71

24.0

4.99

29.1

24.28

12.0

18.71

34.3

32.35

37.2

2.42

17.3

3.84

34.7

24.78

51.9

14.60

31.1

34.31

22.8

10.67

17.1

2.66

29.9

14.10

22.2

25.58

19.5

39.98

33.5

29.24

31.6

ΣX=302.2

ΣY=448.2

ΣX=

Σ=

Σ=

Σ=

Σ=

Mean X =

Mean Y =

Variance (Y)  =

Standard deviation (Y) =

Variance (X)  =

Standard deviation (Y) =

Covariance (X,Y) =

*Answers may differ due to rounding (2 decimal points); however the exact value of these column totals, properly calculated will always be equal to zero.

Sources: The World Bank Group, Development Education Program Learning Model: Economics, GNP per Capita, 2004. International Social Survey Programme, 2000.

2.      From the table that you created in #5, calculate a, b, and write out the regression equation (i.e., prediction equation) (10 pts).

3.      Calculate and interpret error type, E2 (5 pts).

% Willing to Pay Higher Taxes (Y)

Predicted % Willing to Pay Higher Taxes (Ŷ)

(Y- Ŷ)

 (Y- Ŷ)²

31.6

29.58

34.3

27.99

51.9

28.90

22.8

30.34

19.5

29.02

29.9

25.56

31.1

27.36

24.0

28.14

37.2

30.04

22.2

27.29

17.3

25.53

17.1

26.77

29.1

25.91

33.5

31.20

12.0

28.83

34.7

25.74

Σ=

Using your answer from #7, calculate the PRE measure, r². Interpret (5 pts).

4.      About what percentage of citizens are willing to pay higher taxes for a country with a GNP per capita of 3.0 (i.e., $3,000)? For a GNP per capita of 30.0 (i.e., $30,000) (10 pts)?

Problem set 3: use the following information to answer questions 10-12 (30 points total):

Calculate the Y-intercept, a, of the regression equation using the following information: (10 pts) Mean number of years of schooling: 17

Mean monthly income: $2,750

Slope, b, of the regression equation: $650

5.      Consider the following linear regression prediction equation: Y = 12 + -1x. If x = 7, what is the predicted value of, Y, for this observation (10 pts)?

6.      Consider the following linear regression prediction equation: Y = 12 + -1x. If the predicted value of, Y, for an observation is 5, calculate the residual for an observation where the observed value, Y, is equal to 9 (10 pts)?