SUMMARY OUTPUT Regression Statistics Multiple R 0.926205402 R Square 0.857856447 Adjusted R Square 0.82626899 Standard Error 0.405072431 Observations 12 ANOVA df SS MS F Significance F Regression 2 8.912414 4.456207 27.15813641 0.000153912 Residual 9 1.476753 0.164084 Total 11 10.38917 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0.402657005 0.284579 1.414924 0.19074504 -0.241104346 1.046418 -0.2411 1.046418 Year 0.044109996 0.041808 1.055049 0.318901086 -0.050467369 0.138687 -0.05047 0.138687 # of tourist Million 0.14263285 0.026956 5.291348 0.000499541 0.081654453 0.203611 0.081654 0.203611
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The regression equation is given as: \[ \text{Number of tourists} = 0.402 + 0.044 \times \text{Year} \] Show more…
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Bus and subway ridership in New York City during the summer months is believed to be heavily tied to the number of tourists visiting the city. During the past 12 years, the following data have been obtained: Based on linear regression, answer the following: a. What is the regression line? b. What is the MAD? c. What is the expected ridership if nine million tourists visit the city? c. What is the expected ridership if twenty five million tourists visit the city?
Krishna G.
Do a complete regression analysis by performing these steps. a. Draw a scatter plot. b. Compute the correlation coefficient. c. State the hypotheses. d. Test the hypotheses at $\alpha=0.05 .$ Use Table I. e. Determine the regression line equation if $r$ is significant. $f$. Plot the regression line on the scatter plot, if appropriate. g. Summarize the results. Television Viewers A television executive selects 10 television shows and compares the average number of viewers the show had last year with the average number of viewers this year. The data (in millions) are shown. Describe the relationship. $$ \begin{array}{l|ccccc} \text { Viewers last year } x & 26.6 & 17.85 & 20.3 & 16.8 & 20.8 \\ \hline \text { Viewers this year } y & 28.9 & 19.2 & 26.4 & 13.7 & 20.2 \\ \text { Viewers last year } x & 16.7 & 19.1 & 18.9 & 16.0 & 15.8 \\ \hline \text { Viewers this year } y & 18.8 & 25.0 & 21.0 & 16.8 & 15.3 \end{array} $$
Correlation and Regression
Regression
SIMPLE REGRESSION Use the Regression option in Data Analysis in Excel to produce the appropriate simple regression output for the data set supplied in the Excel spreadsheet. (12 pts) b. Write out the estimated regression equation. Use the appropriate variable names (those in the excel spreadsheet) to label things. (5 pts) c. Interpret the estimated slope coefficient. (4 pts) d. Predict the value of the dependent variable when the value of the independent variable equals its mean. (5 pts) Identify an anticipated direction for the relationship between the two variables in this scenario. Test whether the results based upon the sample data support your anticipated population expectation. Use alpha = 0.05. (15 pts) f. Test, using a MODEL test, whether or not there is a linear relationship between the dependent and independent variables. Use alpha = 0.01. (15 pts) g. Construct a 90% confidence interval for the true population slope coefficient, B1. (6 pts) h. Interpret the interval created in part g. (4 pts) i. Confirm that the calculated t for the slope coefficient is the square root of the calculated F statistic. (4 pts) j. Confirm that the calculated t for the correlation coefficient equals the calculated t for the slope coefficient. (4 pts) k. Create the normal probability plot for the model. (5 pts) Does it look like the error term assumption associated with this plot is valid? (5 pts) m. Create the residual plot for the independent variable. (5 pts) Does it look like the assumption associated with this plot is valid? (5 pts)
Sri K.
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