Question

Refer to the data below which contains the percentage change​ (X) in a stock market index over the first five trading days of the year and percentage change​ (Y) in the index over the whole year. Complete parts a and b.

​(X)	1.4	0.3	−0.2	2.9	2.2	−1.9	−1.5	5.4	−1.6	1.4	1.7	−4.8	−0.1
​(Y)	14.9	−9.4	19.4	20.3	−3.8	27.6	22.4	2.4	11.9	28	−4.4	20.5	−0.3

a. Estimate the linear regression of Y on X.

Yi=_______ +(______)Xi

​(Round to four decimal places as​ needed.)

b. Provide interpretations of the intercept and slope of the sample regression line.

For a one percent gain or loss ? over the first five trading days of the​ year, estimates would predict a change of ______%  over the whole year. If there is a zero percent change over the first five trading days of the​ year, estimates would predict a change of ___________​% over the whole year.

Answer 1

a.

Х- М., V.MN (Х- Му)? (Х- М.ХҮ-М) е н о л со om in m л ооо оо л со уоu са о о л вно носа о о в е уол муо: UwNNO ш о л н м -15.9 1.69 -0.8 16.5 - 20.67 - 46.8 5.9 27.04 л Ss: 78.74 SP: -153.9

Sum of X = 5.2
Sum of Y = 149.5
Mean X = 0.4
Mean Y = 11.5
Sum of squares (SS_X) = 78.74
Sum of products (SP) = -153.9

Regression Equation = ŷ = bX + a

b = SP/SS_X = -153.9/78.74 = -1.9545

a = M_Y - bM_X = 11.5 - (-1.95*0.4) = 12.2818

ŷ = -1.9545X + 12.2818

b. For a one percent loss over the first five trading days of the​ year, estimates would predict a change of -1.9545%  over the whole year.

If there is a zero percent change over the first five trading days of the​ year, estimates would predict a change of 12.2818​% over the whole year.