Problem set 4: use the following information to answer questions 11-15 (15 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 12.4 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 (5 pts).

GNP per Capita (X)	% Willing to Pay Higher Taxes (Y)	(X-)	(X-)2	(Y-)	(Y-) 2	(X-) (Y-)
21.22	25.6
26.58	17
14.56	13.8
37.55	35.43
1.88	18.7
4.62	33.52
28.8	45.8
15.7	33.5
30.12	24.6
11.52	18.9
3.77	25.3
16.5	24.8
29.82	17.14
36.83	31.32
30.53	36.59
X=310.00	Y=402.00	X=	=	=	=	=
Mean X = X / N = ; Please make sure you get the correct N and N is 15 in this data.
Mean Y = Y / N =
Variance (X) =S2X = (X-)2/ N-1 = Standard deviation (X) =Sx = square root ( ) =
Variance (Y) =S2Y = (Y-) 2/ N-1 = Standard deviation (Y) =Sy = square root ( ) =
Covariance (X,Y) = Sxy = (X-) (Y-) / N-1 =
*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.

1. From the table that you created in #11, calculate a, b, and write out the regression equation (i.e., prediction equation) (3 pts).

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

% Willing to Pay Higher Taxes (Y)	Predicted % Willing to Pay Higher Taxes ()	(Y- )	(Y- )2
25.60	26.94
17.00	28.28
13.80	25.27
35.43	31.02
18.70	22.10
33.52	22.79
45.80	28.83
33.50	25.56
24.60	29.16
18.90	24.51
25.30	22.57
24.80	25.76
17.14	29.09
31.32	30.84
36.59	29.26
			=

1. Using your answer from #13, calculate the PRE measure, r². Interpret (2 pts).

1. About what percentage of citizens are willing to pay higher taxes for a country with a GNP per capita of 4.0 (i.e., $4,000)? For a GNP per capita of 36.0 (i.e., $36,000) (2 pts)?