Find the coefficient of determination, given that the value of the linear correl

Question

Find the coefficient of determination, given that the value of the linear correlation coefficient, r, is 0.738.

Select one:

a. 0.545

b. 0.738

c. 0.262

d. 0.455

The equation of the regression line for the paired data below is y = 3x and the standard error of the estimate is se = 2.2361. Find the 90% prediction interval of y for x = 3.
x              2              4              5              6
y              7              11           13           20

Select one:

a. 6.8 < y < 11.2

b. 1.2 < y < 16.8

c. 4.5 < y < 13.5

d. 7.1 < y < 10.9

Explanation / Answer

Q.1) Given that, correlation coefficient r = 0.738

To find coefficient of determination R2 = r * r = 0.738 * 0.738 = 0.545

Answer: a) 0.545

Q.2) Regression equation y = 3x

Standard error of estimate se = 2.2361

To find the 90% prediction interval of x=3

Prediction intetval formula is,

Y-pred +/- t-critical * se

Answer: b) 1.2 < y < 16.8

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