Question

1. Here is a bivariate data set.

x	y
49.7	34.8
43.9	30.9
48	30
46.3	32
46.9	30.3
46.2	34.6

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.
r² = %

2. You run a regression analysis on a bivariate set of data (n=71). With ¯x=58.8 and ¯y=34.3, you obtain the regression equation

y=−0.996x+3.479

with a correlation coefficient of r=−0.206r=-0.206. You want to predict what value (on average) for the response variable will be obtained from a value of 20 as the explanatory variable.

What is the predicted response value?
y =

(Report answer accurate to one decimal place.)

3.Match each scatterplot shown below with one of the four specified correlations.

• -abcd
• -abcd
• -abcd
• -abcd

Answer 1

1.

x	y	XY	X²	Y²
49.7	34.8	1729.56	2470.09	1211.04
43.9	30.9	1356.51	1927.21	954.81
48	30	1440	2304	900
46.3	32	1481.6	2143.69	1024
46.9	30.3	1421.07	2199.61	918.09
46.2	34.6	1598.52	2134.44	1197.16
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
281	192.6	9027.26	13179.04	6205.1

Sample size, n =	6
x̅ = Ʃx/n =	46.8333
y̅ = Ʃy/n =	32.1
SSxx = Ʃx² - (Ʃx)²/n =	18.8733
SSyy = Ʃy² - (Ʃy)²/n =	22.64
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	7.16

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 0.346

Coefficient of determination, r² = (SSxy)²/(SSxx*SSyy) = 0.1200 = 12%

-----------------------------------

2. y = −0.996 x + 3.479

At x = 20, predicted y =

y = −0.996 * 20 + 3.479 = -16.4