For a sample of 20 monthly observations a financial analyst wants to regress the

Question

For a sample of 20 monthly observations a financial analyst wants to regress the percentage rate of return (Y) of the common stock of a corporation on the percentage rate of return (X) of the Standard and Poor's 500 index. The following information is available:

a) Estimate the linear regression of Y on X.

b) Interpret the slope of the sample regression line.

c) Interpret the intercept of the sample regression line.

I have the textbook answer but I'm not sure how they got there; can anyone help me with this question?? Thank you!!

For a sample of 20 monthly observations a financial analyst wants to regress the percentage rate of return (Y) of the common stock of a corporation on the percentage rate of return (X) of the Standard and Poor's 500 index. The following information is available: Summation yi limit i=1 to 20 = 22.6, summation xi limit i=1 to 20= 25.4,summation xi^2 limit i=1 to 20= 145.7, summation xiyi limit i=1 to 20 = 150.5 a) Estimate the linear regression of Y on X. b) Interpret the slope of the sample regression line. c) Interpret the intercept of the sample regression line. I have the textbook answer but I'm not sure how they got there; can anyone help me with this question?? Thank you!!

Explanation / Answer

linear regression model :

Y = + X +

a) the least square estimate of = [(xi-xbar)(yi-ybar)] /[(xi-xbar)2] = [(xiyi) - (xi)* (yi)]/[(xi2) - (xi)] = -3.52

the least square estimate of = ybar-(estimate of )*xbar = 5.6

b) the slope is negative . it means that when x increases y is likely to decrease

c) intercept on y axis is = 5.6 . so, it means when there is 0 amount of x then the amount of y is 5.6

intercept on x axis is (-/) = 1.59

which means when amount of x is 1.59 the output y is 0

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