Question

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

x	y
15.5	58.8
25.4	62.9
53.7	68.8
46.5	78.6
28.5	57.5
5.7	68.1
-0.4	67.8
43.8	87.7
23.1	64.9
31.3	81.3
48.2	80.1
15.9	71.1

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

2) 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 = ____%

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

y= _______  x + _________

4) Predict what value (on average) for the response variable will be obtained from a value of 12.1 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

The table given below ,

	x	y	x^2	y^2	xy
	15.5	58.8	240.25	3457.44	911.4
	25.4	62.9	645.16	3956.41	1597.66
	53.7	68.8	2883.69	4733.44	3694.56
	46.5	78.6	2162.25	6177.96	3654.9
	28.5	57.5	812.25	3306.25	1638.75
	5.7	68.1	32.49	4637.61	388.17
	-0.4	67.8	0.16	4596.84	-27.12
	43.8	87.7	1918.44	7691.29	3841.26
	23.1	64.9	533.61	4212.01	1499.19
	31.3	81.3	979.69	6609.69	2544.69
	48.2	80.1	2323.24	6416.01	3860.82
	15.9	71.1	252.81	5055.21	1130.49
Sum	337.2	847.6	12784.04	60850.16	24734.77

From table ,

1 ) The correlation coefficient is ,

2)

Therefore , proportion of the variation in y can be explained by the variation in the values of x is 25.9%

3) The regression line is ,

Where , 'a' be the intercept and 'b' be the slope

Therefore ,

y=0.2772*x+62.8440

4) For , x=12.1

y=0.2772*x+62.8440=0.2772*12.1+62.8440=66.1981