Ch 14 #58 **Transcription for Educational Website: Stock Market Performance and Analysis****Supplementary Exercises****55.** Does a high value of \( r^2 \) imply that two variables are causally related? Explain.**56.** In your own words, explain the difference between an interval estimate of the mean value of y for given x, and an interval estimate for an individual value of y for given x.**57.** What is the purpose of testing whether \( \beta = 0 \)? If we reject \( \beta = 0 \), does it imply a good fit?**58. Stock Market Performance.** The Dow Jones Industrial Average (DJIA) and the Standard & Poor's 500 (S&P 500) indexes are used as measures of overall movement in the stock market. The DJIA is based on the price movements of 30 large companies; the S&P 500 index is composed of 500 stocks and is considered a better measure of stock market performance because it is broader-based. Some say the S&P 500 is a better measure because of this. The closing prices for the DJIA and the S&P 500 for 15 weeks of a previous year follow (source: Barron’s website).| Date | DJIA | S&P ||------------|-------|------|| January 6 | 12,360 | 1,278 || January 13 | 12,422 | 1,289 || January 20 | 12,660 | 1,315 || January 27 | 12,960 | 1,316 || February 3 | 12,862 | 1,345 |**Explanation of Table:**The table above displays the closing prices of two major stock market indexes, DJIA and S&P 500, over a span of five weeks. Each row represents the closing prices for a specific date. The DJIA values are in the thousands, indicating the movement of 30 large companies, while the S&P 500 values show the index composition of 500 stocks, offering a broader perspective of the market trends during that time frame. ### Supplementary Exercises**Data Analysis and Regression Exercises****Data:**- **Date:** - February 10 - February 17 - February 24 - March 2 - March 9 - March 16 - March 23 - March 30 - April 5 - April 13- **DJIA:** - 12,861 - 12,950 - 12,983 - 12,922 - 13,081 - 13,212 - 13,060 - 12,850 - — - —- **S&P:** - 1343 - 1362 - 1366 - 1370 - 1371 - 1397 - 1404 - 1398 - 1408 - 1370**Exercises:**a. Develop a scatter diagram with DJIA as the independent variable.b. Develop the estimated regression equation.c. Test for a significant relationship. Use \(\alpha = 0.05\).d. Did the estimated regression equation provide a good fit? Explain.e. Suppose that the closing price for the DJIA is 13,500. Predict the closing price for the S&P 500.f. Should we be concerned that the DJIA value in part (e) is beyond the range of the data used to develop the estimated regression equation?**Source:** Barron's website. [Visit Barron's Website](http://www.barrons.com/aDJIAfile)

Given the data of the closing price for the DJIA and the S&P 500 for 15 weeks, of a previous year as Date DJIA S&P January 6 12360 1278 January 13 12422 1289 January 20 12720 1315 January 27 12660 1316 February 3 12862 1345 February 10 12801 1343 February 17 12950 1362 February 24 12983 1366 March 2 12978 1370 March 9 12922 1371 March 16 13233 1404 March 23 13081 1397 March 30 13212 1408 April 5 13060 1398 April 13 12850 1370 a. Develop a scatter diagram with DJIA as the independent variable : The steps for creating Scatter plot in EXCEL : Upload the data into excel sheet Select the two columns of data Select Insert in the home bar Select Recommended charts from Insert tool bar Select (X,Y) Scatter from all charts in the insert chart ribbon Click OKb. Develop the estimated regression equation : The steps for Regression in EXCEL : Open an EXCEL file. Enter the data values in excel sheet. Select Data in Home bar Select Data Analysis in Data bar Select Regression in Data Analysis tool bar . Input Y range and X range and click labels and confidence levels in Regression ribbon Click OK. Therefore, the estimated regression equation is S&P^=0.1573(DJIA)-699.02c. Test for a significant relationship using α=0.05 The null and alternate hypothesis are H0 : the linear relationship is not significant Ha : the linear relationship is significant p-value=F.DIST.RT(239.8902,1,13)=0.0000 Decision : p-value<0.05, Reject the null hypothesis. Since p-value is less than the significance level, α=0.05. Hence there is significant linear relation between DJIA and S&P. d. The estimated regression equation provide a good fit is determined by checking the coefficient of determination value. The coefficient of determination provides the percentage of variation is explained by the given regression equation. Here, coefficient of determination, R2=0.9486 Which means 94.86% of the variation is explained by the estimated regression equation. Hence the estimated regression equation provide a good fit.e. Suppose that the closing price for the DJIA is 13500, then the closing price for the S&P 500 S&P^=0.1573×13500-699.02=1424.53≈1425 Therefore, for the closing price for the DJIA is 13500, the predicted closing price for the S&P 500 is 1425. f. The range of values for DJIA is 12360, 13233. Since the predicted regression equation is good fit to the data. So we should not be concerned that the DJIA value of 13500 used to predict the S&P 500 value in part (e) is beyond the range of data used to develop the estimated regression equation.

Math

Statistics

Afile 500 Date February 10 February 17 February 24 March 2 March 9 March 16 March 23 March 30 April 5 April 13 DJIA 12,801 12,950 12,983 12,978 12,922 13,233 13,081 13,212 13,060 12,850 Source: Barron's website, (http://www.barrons.com/data) S&P 1343 1362 1366 1370 1371 1404 1397 1408 1398 1370 a. Develop a scatter diagram with DJIA as the independent variable. b. Develop the estimated regression equation. c. Test for a significant relationship. Use a = .05. d. Did the estimated regression equation provide a good fit? Explain. e. Suppose that the closing price for the DJIA is 13,500. Predict the closing price for the S&P 500. f. Should we be concerned that the DJIA value of 13,500 used to predict the S&P 500 value in part (e) is beyond the range of the data used to develop the estimated