Question

Run a regression analysis on the following bivariate set of data with y as the response variable.

x	y
48	41.8
39.2	67.4
34.7	68.4
42.9	50.2
49	50.6
45.6	57
58.7	29.7
40.5	68.4
47.4	34.7
45.7	50.9
38.9	47.7
40.9	53.6

Find the correlation coefficient and report it accurate to three decimal places.
r =

What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5%...you would enter 84.5 without the percent symbol.)
r² = %

Based on the data, calculate the regression line (each value to three decimal places)

y =  x +

13.Predict what value (on average) for the response variable will be obtained from a value of 40.5 as the explanatory variable. Use a significance level of α=0.05α=0.05 to assess the strength of the linear correlation.

What is the predicted response value? (Report answer accurate to one decimal place.)
y =

Answer 1

	SUMMARY OUTPUT
	Regression Statistics
	Multiple R	0.80159
	R Square	0.642546
	Adjusted R Square	0.606801
	Standard Error	7.857172
	Observations	12
	ANOVA
		df	SS	MS	F	Significance F
	Regression	1	1109.729	1109.729	17.97564	0.001717
	Residual	10	617.3515	61.73515
	Total	11	1727.08
		Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
	Intercept	122.7141	16.90241	7.260157	2.73E-05	85.05322	160.3751	85.05322	160.3751
	x	-1.60333	0.378164	-4.23977	0.001717	-2.44593	-0.76073	-2.44593	-0.76073