b) If the correlation coefficient of the data above is-0.806; determine if a lin

Question

b) If the correlation coefficient of the data above is-0.806; determine if a linear relation exits between the age and irrelevant answers. (Hint: use table I1) c) Determine the coefficient of determination and interpret its meaning (write your answer in percent with one decimal place) d) The regression equation of the above data is y--0.732x+13.192. Interpret the slope of the regression line. (hit: b =-0.732 =-0.732) using the regression equation, y=-0.732x+13.192, to predict the value of irrelevant answers when the age is 15 years. Write your answer as whole number e)

Explanation / Answer

(b) Here r = -0.806

so we have t value

t = r sqrt [(n-2) / (1 - r2 )]]

n = 10 here

t = -0.806 * sqrt [ 8/ (1 - 0.8062 )]

t = 3.85

tcritical  for dF = 8 and alpha = 0.05 => 2.30

so it is statistically significant correlation.

(c) COefficient of determination = R2 = (-0.806)2 = 0.6496

so here we can say that 64.96% of variation in irrelaevant answers is predicted by the age of the person.

(d) y = -0.732 x + 13.192

that line entails that if there is an increase of one year in age then it will decrease the number of irrelevant answers by 0.732.

(e) at the age = 15 years

y^ = - 0.732x + 13.192

y^ = -0.732 * 15 + 13.192

y^ = 2.21 answers or say 2 irrelevent answers

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