1) Suppose the least squares solution to Y = beta(0) + beta(1)X is beta(0) = -5

Question

1) Suppose the least squares solution to Y = beta(0) + beta(1)X is beta(0) = -5 and beta(1) = 7

a) When X = 6 the predicted value of Y is 37.

b) When X = 6 the estimate for the mean value of Y is 37.

c) Both (a) and (b).

d) None of the above.

2) Which of the following is not true.

a) -1 cor(x, y) 1.

b) cor(x, y) = cor(y, x)

c) cor(x, y) measures the strength of any relationship between x and y.

d) The closer cor(x, y) is to zero, the weaker the linear relationship between x and y.

Please answer all questions, I will be sure to give you thumb up!

Explanation / Answer

(1) Given, the least squares solution to Y = beta(0) + beta(1)X is beta(0) = -5 and beta(1) = 7.
If we put X = 6, in the above equation, we get the predicted value of Y as Y = -5 + (7 * 6) = -5 + 42 = 37.
Also, the predicted value of Y refers to the estimate for the mean value of Y. Hence, the estimate for the mean value of Y will also be 37.
Hence, correct answer is (c) Both (a) and (b).

(2) Here, correct answer is (c) cor(x, y) measures the strength of any relationship between x and y.
This is due to the fact that cor(x,y) is measured via Pearson product-moment correlation coefficient (also known as r, R, or Pearson's r), which is a measure of the strength and direction of the linear relationship between two variables.

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