Chapter 13 - Simple+Linear+Regression

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SUMMARY OUTPUT Regression Statistics Multiple R 0.920797850609979 R Square 0.847868681687957 Adjusted R Square 0.83519107182862 Standard Error 0.999298362726938 Observations 14 ANOVA df SS MS F ignificance F Regression 1 66.7854 66.7854 66.87922 3E-06 Residual 12 11.98317 0.998597 Total 13 78.76857 Coefficients tandard Erro t Stat P-value Lower 95%Upper 95% Lower 95.0% Intercept -1.20883909262412 0.994874 -1.215067 0.247707 -3.376484 0.958806 -3.376484 Profiled Customers 2.07417291676253 0.253629 8.177972 3E-06 1.521562 2.626784 1.521562 RESIDUAL OUTPUT PROBABILITY OUTPUT Observation Predicted Annual Sales Residuals ndard Residuals PercentileAnnual Sales 1 6.46560069939723 -0.765601 -0.797422 3.571429 3.5 2 6.25818340772098 -0.358183 -0.373071 10.71429 4.1 3 4.59884507431095 2.101155 2.188487 17.85714 4.7 4 10.406529241246 -0.906529 -0.944208 25 4.9 5 5.63593153269222 -0.235932 -0.245738 32.14286 5.4 6 3.35434132425344 0.145659 0.151713 39.28571 5.7 7 5.63593153269222 0.564068 0.587513 46.42857 5.9 8 5.22109694933971 -0.521097 -0.542756 53.57143 6.1 9 5.42851424101597 0.671486 0.699395 60.71429 6.2 10 6.05076611604472 -1.150766 -1.198596 67.85714 6.7 11 9.57686007454102 1.12314 1.169822 75 7.6 12 8.33235632448351 -0.732356 -0.762796 82.14286 9.5 13 10.8213638245985 0.978636 1.019312 89.28571 10.7 14 5.01367965766346 -0.91368 -0.951656 96.42857 11.8 0 2 4 6 8 10 12 14 Normal Probability Plo Annual Sales
0 20 40 60 80 0 Sample Percentile
Upper 95.0% 0.958806 2.626784 2 2.5 3 3.5 4 4.5 5 5.5 6 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Profiled Customers Residual Plot Profiled Customers Residuals 2 2.5 3 3.5 4 4.5 5 5.5 6 0 2 4 6 8 10 12 14 Profiled Customers Line Fit Plot Annual Sales Predicted Annual Sales Profiled Customers Annual Sales ot
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100 120
Profiled Customers Annual Sales 3.7 5.7 3.6 5.9 2.8 6.7 5.6 9.5 3.3 5.4 2.2 3.5 3.3 6.2 3.1 4.7 3.2 6.1 3.5 4.9 5.2 10.7 4.6 7.6 5.8 11.8 3 4.1
Simple Linear Regression Regression Statistics Multiple R 0.9208 R Square 0.8479 Adjusted R Square 0.8352 Standard Error 0.9993 Observations 14 ANOVA df SS MS F Significance F Regression 1 66.7854 66.7854 66.8792 0.0000 Residual 12 11.9832 0.9986 Total 13 78.7686 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -1.2088 0.9949 -1.2151 0.2477 -3.3765 0.9588 Profiled Customers 2.0742 0.2536 8.1780 0.0000 1.5216 2.6268
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Calculations b1, b0 Coefficients 2.0742 -1.2088 b1, b0 Standard Error 0.2536 0.9949 R Square, Standard Error 0.8479 0.9993 F, Residual df 66.8792 12.0000 Regression SS, Residual SS 66.7854 11.9832 Confidence level 95% 2.1788 2.1676 0.5526 Lower 95% Upper 95% -3.3765 0.95881 1.5216 2.62678 t Critical Value Half Width b0 Half Width b1
Observation X Y Residuals 1 1.7 2.31725486587 3.7 1.3827451341 2 1.6 2.1098375742 3.9 1.7901624258 3 2.8 4.59884507431 6.7 2.1011549257 4 5.6 10.4065292412 9.5 -0.9065292412 5 1.3 1.48758569917 3.4 1.9124143008 6 2.2 3.35434132425 5.6 2.2456586757 7 1.3 1.48758569917 3.7 2.2124143008 8 1.1 1.07275111581 2.7 1.6272488842 9 3.2 5.42851424102 5.5 0.071485759 10 1.5 1.90242028252 2.9 0.9975797175 11 5.2 9.57686007454 10.7 1.1231399255 12 4.6 8.33235632448 7.6 -0.7323563245 13 5.8 10.8213638246 11.8 0.9786361754 14 3.0 5.01367965766 4.1 -0.9136796577 Predicted Y
Durbin-Watson Statistic Sum of Squared Difference of Residuals 30.9549 Sum of Squared Residuals 31.1869 Durbin-Watson Statistic 0.9926
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Confidence Interval Estimate and Prediction Interval Data X Value 4 Confidence Level 95% Intermediate Calculations Sample Size 14 Degrees of Freedom 12 2.1788 Sample Mean 3.7786 Sum of Squared Difference 15.5236 Standard Error of the Estimate 0.9993 0.0746 Predicted Y (YHat) 7.0879 For Average Y Interval Half Width 0.5946 Confidence Interval Lower Limit 6.4932 Confidence Interval Upper Limit 7.6825 For Individual Response Y Interval Half Width 2.2570 Prediction Interval Lower Limit 4.8308 Prediction Interval Upper Limit 9.3449 t Value h Statistic
Simple Linear Regression Regression Statistics Multiple R =SQRT(C12/C14) R Square =L4 Adjusted R=1 - (B14/B13) * (C13/C14) Standard E=M4 Observatio=COUNT(SLRData!A:A) ANOVA df SS MS F Significance F Regression 1 =L6 =L6 =L5 =F.DIST.RT(E12, B12, B13) Residual =M5 =M6 =C13/B13 Total =B12 + B13 =C12 + C13 Coefficients andard Err t Stat P-value wer " & L8 * 100 per " & L8 * 100 & wer " & L8 * 100 Intercept =M2 =M3 =B17/=T.DIST.2T(ABS(=B17 - L10 =B17 + L10 =F17 =SLRData! =L2 =L3 =B18/=T.DIST.2T(ABS(=B18 - L11 =B18 + L11 =F18
Calculations b1, b0 Coefficie =LINEST(SLRData!B2:B15, SLRD=LINEST(SLRData!B2:B15, SLRData!A2:A15 b1, b0 Standard =LINEST(SLRData!B2:B15, SLRD=LINEST(SLRData!B2:B15, SLRData!A2:A15 R Square, Stan =LINEST(SLRData!B2:B15, SLRD=LINEST(SLRData!B2:B15, SLRData!A2:A15 F, Residual df =LINEST(SLRData!B2:B15, SLRD=LINEST(SLRData!B2:B15, SLRData!A2:A15 Regression SS, =LINEST(SLRData!B2:B15, SLRD=LINEST(SLRData!B2:B15, SLRData!A2:A15 Confidence leve 95% =T.INV.2T(1 - L8, B13) =L9 * C17 =L9 * C18 per " & L8 * 100 & "%" =G17 =G18 t Critical Value Half Width b0 Half Width b1
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5, TRUE, TRUE) 5, TRUE, TRUE) 5, TRUE, TRUE) 5, TRUE, TRUE) 5, TRUE, TRUE)
Observation X Y Residuals 1 1.7 =COMPUTE!$B$18 * B2 + COMPUTE!$B$17 3.7 =D2 - C2 2 1.6 =COMPUTE!$B$18 * B3 + COMPUTE!$B$17 3.9 =D3 - C3 3 2.8 =COMPUTE!$B$18 * B4 + COMPUTE!$B$17 6.7 =D4 - C4 4 5.6 =COMPUTE!$B$18 * B5 + COMPUTE!$B$17 9.5 =D5 - C5 5 1.3 =COMPUTE!$B$18 * B6 + COMPUTE!$B$17 3.4 =D6 - C6 6 2.2 =COMPUTE!$B$18 * B7 + COMPUTE!$B$17 5.6 =D7 - C7 7 1.3 =COMPUTE!$B$18 * B8 + COMPUTE!$B$17 3.7 =D8 - C8 8 1.1 =COMPUTE!$B$18 * B9 + COMPUTE!$B$17 2.7 =D9 - C9 9 3.2 =COMPUTE!$B$18 * B10 + COMPUTE!$B$17 5.5 =D10 - C10 10 1.5 =COMPUTE!$B$18 * B11 + COMPUTE!$B$17 2.9 =D11 - C11 11 5.2 =COMPUTE!$B$18 * B12 + COMPUTE!$B$17 10.7 =D12 - C12 12 4.6 =COMPUTE!$B$18 * B13 + COMPUTE!$B$17 7.6 =D13 - C13 13 5.8 =COMPUTE!$B$18 * B14 + COMPUTE!$B$17 11.8 =D14 - C14 14 3.0 =COMPUTE!$B$18 * B15 + COMPUTE!$B$17 4.1 =D15 - C15 Predicted Y
Durbin-Watson Statistics Sum of Squared Difference of Residuals =SUMXMY2(RESIDUALS!E3:E15,RESIDUALS!E2:E14) Sum of Squared Residuals =SUMSQ(RESIDUALS!E2:E15) Durbin-Watson Statistic =B3/B4
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Confidence Interval Estimate and Prediction Interval Data X Value 4 Confidence Level 95% Intermediate Calculations Sample Size =COUNT(SLRData!A:A) Degrees of Freedom =B8 - 2 =T.INV.2T(1 - B5, B9) Sample Mean =AVERAGE(SLRData!A:A) Sum of Squared Difference =DEVSQ(SLRData!A:A) Standard Error of the Estimate =COMPUTE!B7 =1/B8 + (B4 - B11)^2/B12 Predicted Y (YHat) =TREND(SLRData!B2:B15, SLRData!A2:A15, B4) For Average Y Interval Half Width =B10 * B13 * SQRT(B14) Confidence Interval Lower Limit =B15 - B18 Confidence Interval Upper Limit =B15 + B18 For Individual Response Y Interval Half Width =B10 * B13 * SQRT(1 + B14) Prediction Interval Lower Limit =B15 - B23 Prediction Interval Upper Limit =B15 + B23 t Value h Statistic

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A regression analysis was performed and the summary output is shown below.   Regression Statistics Multiple R 0.7802268560.780226856 R Square 0.6087539470.608753947 Adjusted R Square 0.5870180550.587018055 Standard Error 6.7217061336.721706133 Observations 2020     ANOVA   dfdf SSSS MSMS F� Significance F� Regression 11 1265.3871265.387 1265.3871265.387 28.006928.0069 4.9549E-054.9549E-05 Residual 1818 813.264813.264 45.18145.181     Total 1919 2078.6512078.651           Step 1 of 2:  How many independent variables are included in the regression model
A regression analysis was performed and the summary output is shown below.   Regression Statistics Multiple R 0.7802268560.780226856 R Square 0.6087539470.608753947 Adjusted R Square 0.5870180550.587018055 Standard Error 6.7217061336.721706133 Observations 20     ANOVA   dfdf SSSS MSMS F� Significance F� Regression 11 1265.3871265.387 1265.3871265.387 28.006928.0069 4.9549E-054.9549E-05 Residual 1818 813.264813.264 45.18145.181     Total 1919 2078.6512078.651           Step 2 of 2:  Which measure is appropriate for determining the proportion of variation in the dependent variable explained by the set of independent variable(s) in this model?
What is correlation and regression? What information does it provide? Why is it important?    What does this regression analaysis tell us? What is the significance of the coeffecients?
Analysis of Variance Source DF SS MS Regression 1 Residual Error 13 0.2364 Total 14 11.3240 What is the value for MSR (Mean Square for Regression)?
In an ANOVA table for a multiple regression analysis, total variation is separated into Multiple Choice treatment and error variation treatment and block variation block and error variation regression and residual variation
Analysis of Variance Source DF SS MS Regression 1 Residual Error 13 0.2364 Total 14 11.3240 What is the value of SSE (Sums of Square Residual Error)?
Conduct a global test on the set of independent variables. Interpret   Regression Statistics               Multiple R 0.87027387               R Square 0.75737661               Adjusted R Square 0.75615535               Standard Error 14.6932431               Observations 600                                 ANOVA                   df SS MS F Significance F       Regression 3 401662.063 133887.354 620.160683 8.708E-183       Residual 596 128671.271 215.891394           Total 599 530333.333                                 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -3.9995369 3.05935528 -1.3073137 0.19161031 -10.007965 2.00889078 -10.007965 2.00889078 Annual Income 0.0002132 3.1402E-05 6.78944156 2.7269E-11 0.00015153 0.00027487 0.00015153 0.00027487 Married 45.7808695 1.20203164 38.0862434 8.444E-162 43.4201368 48.1416023 43.4201368 48.1416023 Male 21.9175699 1.20122625 18.2459964 2.0045E-59…
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