Question

# 1. Here is a bivariate data set. x y 49.7 34.8 43.9 30.9 48 30 46.3...

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

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

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