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Worksheet #10 An analyst for a shopping district would like to determine the rent that should be charged for retail spaces depending on how close they are to parking. The analyst takes a random sample of retail spaces in similar shopping districts and measures the monthly rent ($) and distance from parking (in yards) for each retail space. This is the same regression you worked with in Worksheet #9. Here is the complete Excel output for this regression: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept Distance. 0.7076 0.5007 0.4918 978.8761 df 1 56 57 58 SS 53809748.97 53659115.74 107468864.7 Coefficients Standard Error 15003.10 -11.42 249.3464 1.5239 MS 53809748.97 958198.4954 t Stat 60.17 -7.49 F 56.1572 P-value 1.4E-52 5.28E-10 Significance F 5.28E-10 Lower 95% 14503.59 -14.47 Upper 95% 15502.6 -8.37 NOTE: Excel uses scientific notation for very small numbers. So the p-value = 5.28E-10 = 5.28 x 10-10 = 0.000000000528. In the hypothesis test, you may truncate that to 0.000. Very tiny p-values with more than four zeroes after the decimal are often expressed as 0.000 or .000 when they are reported and interpreted. 1

Worksheet #10 An analyst for a shopping district would like to determine the rent that should be charged for retail spaces depending on how close they are to parking. The analyst takes a random sample of retail spaces in similar shopping districts and measures the monthly rent ($) and distance from parking (in yards) for each retail space. This is the same regression you worked with in Worksheet #9. Here is the complete Excel output for this regression: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept Distance. 0.7076 0.5007 0.4918 978.8761 df 1 56 57 58 SS 53809748.97 53659115.74 107468864.7 Coefficients Standard Error 15003.10 -11.42 249.3464 1.5239 MS 53809748.97 958198.4954 t Stat 60.17 -7.49 F 56.1572 P-value 1.4E-52 5.28E-10 Significance F 5.28E-10 Lower 95% 14503.59 -14.47 Upper 95% 15502.6 -8.37 NOTE: Excel uses scientific notation for very small numbers. So the p-value = 5.28E-10 = 5.28 x 10-10 = 0.000000000528. In the hypothesis test, you may truncate that to 0.000. Very tiny p-values with more than four zeroes after the decimal are often expressed as 0.000 or .000 when they are reported and interpreted. 1

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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4) Calculate the Coefficient of Determination: R² = SSR Confirm that this is the same value Excel SST reported in the Regression Statistics table (the top table in the output). Interpret R² in words. 5) Calculate the Standard Error of the Estimate, s = √MSE. Confirm that this is the same value Excel reported in the Regression Statistics table (the top table in the output above). Interpret s in words. 6) Calculate the correlation Coefficient, Rxy = √R². Confirm that this is the same value Excel reported in the Regression Statistics table (the top table in the output above). Interpret Rxy in words, using the rule of thumb from lecture. Here another set of regression results, for a generic DV called y and a generic IV called x. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept X 0.09855694 0.00 -0.0040405 20.5897879 df 1 72 73 74 Coefficients 44.3618365 -0.1587303 More questions on back → MS SS F 299.3986 299.3986 0.70623 30523.63 423.9394 30823.03 Significance F 0.40348 Standard Error t Stat P-value Lower 95% 5.205352 8.522351 1.62E-12 33.98516 0.18888 Upper 95% 54.73852 -0.84037 0.40348 -0.53526 0.217796 3 7) How many observations were in this dataset? 8) Follow the four steps in Ch 14: Handout # 2 to perform the hypothesis test to answer the following question: Is there a statistically significant relationship between y and x? Use an a = 0.05 significance level. The guidelines from the test in Question #1 apply here too. 9) Given your result in Question #8, is it appropriate to continue interpreting this model?
Transcribed Image Text:4) Calculate the Coefficient of Determination: R² = SSR Confirm that this is the same value Excel SST reported in the Regression Statistics table (the top table in the output). Interpret R² in words. 5) Calculate the Standard Error of the Estimate, s = √MSE. Confirm that this is the same value Excel reported in the Regression Statistics table (the top table in the output above). Interpret s in words. 6) Calculate the correlation Coefficient, Rxy = √R². Confirm that this is the same value Excel reported in the Regression Statistics table (the top table in the output above). Interpret Rxy in words, using the rule of thumb from lecture. Here another set of regression results, for a generic DV called y and a generic IV called x. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept X 0.09855694 0.00 -0.0040405 20.5897879 df 1 72 73 74 Coefficients 44.3618365 -0.1587303 More questions on back → MS SS F 299.3986 299.3986 0.70623 30523.63 423.9394 30823.03 Significance F 0.40348 Standard Error t Stat P-value Lower 95% 5.205352 8.522351 1.62E-12 33.98516 0.18888 Upper 95% 54.73852 -0.84037 0.40348 -0.53526 0.217796 3 7) How many observations were in this dataset? 8) Follow the four steps in Ch 14: Handout # 2 to perform the hypothesis test to answer the following question: Is there a statistically significant relationship between y and x? Use an a = 0.05 significance level. The guidelines from the test in Question #1 apply here too. 9) Given your result in Question #8, is it appropriate to continue interpreting this model?
Worksheet #10 An analyst for a shopping district would like to determine the rent that should be charged for retail spaces depending on how close they are to parking. The analyst takes a random sample of retail spaces in similar shopping districts and measures the monthly rent ($) and distance from parking (in yards) for each retail space. This is the same regression you worked with in Worksheet #9. Here is the complete Excel output for this regression: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept Distance. 0.7076 0.5007 0.4918 978.8761 n = df 1 56 57 58 SS 53809748.97 53659115.74 107468864.7 Coefficients Standard Error 15003.10 -11.42 Name: 249.3464 1.5239 MS 53809748 958198.4954 t Stat 60.17 -7.49 F 56.1572 P-value 1.4E-52 5.28E-10 Significance F 5.28E-10 3) Identify the SSR, SSE, and SST on the output on page 1. Lower 95% 14503.59 -14.47 NOTE: Excel uses scientific notation for very small numbers. So the p-value = 5.28E-10 = 5.28 x 10-10= 0.000000000528. In the hypothesis test, you may truncate that to 0.000. Very tiny p-values with more than four zeroes after the decimal are often expressed as 0.000 or .000 when they are reported and interpreted. Upper 95% 15502.6 -8.37 1) Following the four steps in Ch 14: Handout #2, perform the hypothesis test to answer this question: Is there statistically significant relationship between Monthly Rent and Distance from parking? Use an a = 0.05 significance level. You can report the appropriate t test statistic from the output table above, but be aware that you could calculate it by hand using ttest = b₁/S₂. You can show the p-value approach only, and just report the p-value from the output (but the df=n-p-1, same as the SSE, if you want to check the CV approach too :). For the following questions, refer to the Regression Output Equations roadmap and the output above. 2) How many observations were in this dataset? (n = number of observations) 1 SSR = SSE = SST = Which of these is minimized by the regression procedure, in order to determine the slope and intercept of the regression line?
Transcribed Image Text:Worksheet #10 An analyst for a shopping district would like to determine the rent that should be charged for retail spaces depending on how close they are to parking. The analyst takes a random sample of retail spaces in similar shopping districts and measures the monthly rent ($) and distance from parking (in yards) for each retail space. This is the same regression you worked with in Worksheet #9. Here is the complete Excel output for this regression: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept Distance. 0.7076 0.5007 0.4918 978.8761 n = df 1 56 57 58 SS 53809748.97 53659115.74 107468864.7 Coefficients Standard Error 15003.10 -11.42 Name: 249.3464 1.5239 MS 53809748 958198.4954 t Stat 60.17 -7.49 F 56.1572 P-value 1.4E-52 5.28E-10 Significance F 5.28E-10 3) Identify the SSR, SSE, and SST on the output on page 1. Lower 95% 14503.59 -14.47 NOTE: Excel uses scientific notation for very small numbers. So the p-value = 5.28E-10 = 5.28 x 10-10= 0.000000000528. In the hypothesis test, you may truncate that to 0.000. Very tiny p-values with more than four zeroes after the decimal are often expressed as 0.000 or .000 when they are reported and interpreted. Upper 95% 15502.6 -8.37 1) Following the four steps in Ch 14: Handout #2, perform the hypothesis test to answer this question: Is there statistically significant relationship between Monthly Rent and Distance from parking? Use an a = 0.05 significance level. You can report the appropriate t test statistic from the output table above, but be aware that you could calculate it by hand using ttest = b₁/S₂. You can show the p-value approach only, and just report the p-value from the output (but the df=n-p-1, same as the SSE, if you want to check the CV approach too :). For the following questions, refer to the Regression Output Equations roadmap and the output above. 2) How many observations were in this dataset? (n = number of observations) 1 SSR = SSE = SST = Which of these is minimized by the regression procedure, in order to determine the slope and intercept of the regression line?
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