Question

The money raised and spent (both in millions of dollars) by all congressional campaigns for 8 recent 2-year periods are shown in the table. The equation of the regression line is 9 -0.957x + 15.099. Find the coefficient of determination and interpret the result. 4 Money raised, 465.1 Money spent y 443.5 Find the coefficient of determination and interpret the result 655.1 6963 735.8 725.4 798.4 7613 780.8 727.9 1038 3 1016.6 9552 9293 12096 11728 (Round to three decimal places as needed)

Answer 1

	Money raised (x)	Money spent(y)	xy	x2	y2
	465.1	443.5	206271.85	216318.01	196692.25
	655.1	696.3	456146.13	429156.01	484833.69
	735.8	725.4	533749.32	541401.64	526205.16
	798.4	761.3	607821.92	637442.56	579577.69
	780.8	727.9	568344.32	609648.64	529838.41
	1038.3	1016.6	1055535.78	1078066.89	1033475.56
	955.2	929.3	887667.36	912407.04	863598.49
	1209.6	1172.8	1418618.88	1463132.16	1375459.84
Total	6638.3	6473.1	5734155.56	5887572.95	5589681.09

Here

n = 8

The correlation coefficient is given by

$r=\frac{n\sum xy-(\sum x)(\sum y)}{\sqrt{\left [ n\sum x^2-(\sum x)^2 \right ]\left [ n\sum y^2-(\sum y)^2 \right ]}}$

$=\frac{8*5734155.56 -(6638.3 )(6473.1 )}{\sqrt{\left [ 8*5887572.95 -(6638.3 )^2 \right ]\left [ 8*5589681.09 -(6473.1 )^2 \right ]}}$

  

ង 0.3931

The coefficient of determination (R² or r-squared) is a statistical measure in a regression model that determines the proportion of variance in the dependent variable that can be explained by the independent variable.

$r^2=( 0.9931)^2\approx 0.986$

The coefficient of determination is 0.986.

It indicates that 98.6% of the variability in money spent might be explained by variation in money raised.