Question

Professor Nickel is thinking of investing in two stocks: A and B. He has obtained data regarding the closing prices of these stocks on n = five days. Professor Nickel has calculated for this data that Sxx = 236.8, Sxy = -282.4, and error variance = 18.81.

Day Number --- Stock A price/share (x) --- Stock B price/share (y)

1 --- 91 --- 52

2 --- 85 --- 59

3 --- 75 --- 68

4 --- 72 --- 75

5 --- 83 --- 53

(a) Find the estimated regression line for this data.

(b) Find the 95% confidence intervals for the estimated slope and intercept of the regression line.

(c) Calculate R^2.

(d) Professor Nickel believes that there is a negative linear relationship between the price of Stock A and Stock B. To test this hypothesis, he has formed the null hypothesis H0 that the slope of the regression line is zero. Perform a one-sided hypothesis test with H1 that the slope is negative. Test H0 with α = 5%. Can you reject it?

Answer 1

Solution: a. Obtain the regression line MINITAB procedure: Step 1: Choose Stat> Regression > Regression Step 2: In Response, enter the column containing the response (V) variable Step 3: In Predictors, enter the columns containing the predictor () variables. Step 4: Click OK. MINITAB output: Regression Analysis: y versus x The regression equation is y158- 1.19x Coef SE Coef Predictor Constant 150.24 22.97 6.9 0.006 -1.1926 0.2818-4.230.024 8.4.33662 R-sq es.7% R-Sq (adj) 80.9% " " Analysi of Variance 1 336.78 336-78 17.91 0.024 Regression Residual Erro 3 56.42 20. Totai 4 393.20 From the MINITAB output, the regression equation is,

У 158-1.19x obtain the 95% confidence interval. For slope: Here,屆一一1.1926. SE.-0.28 18 Thus, the 95% confidence interval is, SE 1.1926 3.182 x0.2818 = (-2.0893,-0.2959) For intercept: Here, -15824, SEs 22.97 Thus, the 95% confidence interval is, Cİ-A too.SE s -158.24+3.182 x 22.97 -(85.1495,231.3305)

Obtain the value of R From the MINITAB output, the value is, R2-85.7% d. Conduct the test. Null hypothesis: Alternative hypothesis: From the MINITAB output, the p-value for the slope is, p-value = 0.024 Since, p-value <0.05, thus, the null hypothesis is rejected. Therefore, it can be concluded that the claim that there is a negative linear relationship between the price of Stock A and Stock B is true.