1005 ARTSMFI Regression Intro.xlsx - ith Sample Point ith Residual = Predicted = Weekly $ Ad Weekly $ i = b1*Xi b0 ei =Yi i Expense(x Sales(y TREND 1

1005 ARTSMFI Regression Intro.xlsx - ith Sample Point ith...

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TREND 1 63,566 651,334 560,739 90,595 560739.32793697 2 50,762 527,670 #NAME? #NAME? 455214.5368931 3 50,941 523,751 #NAME? #NAME? 456689.77413122 4 17,597 175,467 #NAME? #NAME? 181883.57040062 5 33,029 377,978 #NAME? #NAME? 309067.15173371 6 58,543 520,100 #NAME? #NAME? 519342.02823271 7 60,492 620,856 #NAME? #NAME? 535404.80687567 8 59,686 593,739 #NAME? #NAME? 528762.11852974 189 32,779 211,928 #NAME? #NAME? 307006.76452964 190 49,959 401,212 #NAME? #NAME? 448596.57319362 Total 70,311,201 70,311,201 0 Ybar Equation Yields Same Prediction at Every X Value. Lots of Error with this Model. Ybar = $370,058.95 (PLOT CHART WITH YBAR AND SALES) Yhat Equation Yields Predictions that are MUCH Closer to Sample Points. Much Less Error with this Model. Yhat = $8.24*x + 36,857 (PLOT CHART WITH YHAT AND SALES (X)) Positive Residuals 1 63,566 651,334 560,739 90,595 8.2415488163 2 50,762 527,670 454,184 73,486 3 50,941 523,751 455,052 68,699 4 17,597 175,467 182,701 -7,234 5 33,029 377,978 308,555 69,423 6 58,543 520,100 516,272 3,828 7 60,492 620,856 532,118 88,738 8 59,686 593,739 524,140 69,599 189 32,779 211,928 173,775 38,154 190 49,959 401,212 180,313 220,899 Plot Est. Line Plot Ybar x Predicted Line x Ybar 14,591 14,591 64,717 64,717 i th Sample Point Weekly $ Ad Expense (x) Weekly $ Sales (y) Predicted = ŷ i = b 1 *X i +b 0 i th Residual = e i =Y i - ŷi Note 1: ΣY i = Σŷ i Note 2: Σe i = 0 Lots of Error with this Model. Ybar = $370,058.95 Much Less Error with this Model. Yhat = $8.24*x + 36,857 ith Sample Point Weekly $ Ad Expense (x) Weekly $ Sales (y) Predicted = ŷi = b1*Xi+b0 ith Residual = ei =Yi - ŷi
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ý = $8.24*Xi + $36857.04 Residuals = Distance from Particular Y value to Predicted Value. Estimated Equation can sometimes Overpredict or Underpredict . 10 K 0 K 100 K 200 K 300 K 400 K 500 K 600 K 700 K Weekly $ Sales (y)
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FORMULA 560739.327936968 455214.536893103 456689.77413122 181883.570400617 309067.151733711 519342.028232709 535404.806875672 528762.118529736 307006.764529636 448596.573193617 Slope 8.2415488163 Intercept 36857.0358802413 Negative Residuals Ybar Deviations Ybar Positive Error Ybar Negative Error If we use just Ybar for making predictions, we would not have a very good Model. The Error would be quite big. Yhat = $8.24*x + 36,857
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20 K 30 K 40 K 50 K 60 K 70 K Yhat Weekly $ Sales (y) Weekly $ Ad Expense (x)
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1 63,566 651,334 560,739 90,595 8,207,459,822.33 2 50,762 527,670 455,215 72,456 5,249,854,992.45 3 50,941 523,751 456,690 67,062 4,497,248,247.75 4 17,597 175,467 181,884 -6,417 41,177,379.93 5 33,029 377,978 309,067 68,911 4,748,700,877.09 6 58,543 520,100 519,342 758 574,960.83 7 60,492 620,856 535,405 85,451 7,301,954,249.16 8 59,686 593,739 528,762 64,977 4,222,054,897.28 189 32,779 211,928 307,007 -95,079 9,039,922,019.37 190 49,959 401,212 448,597 -47,385 2,245,319,576.32 Total 70,311,201 70,311,201 0 516,674,372,690 Ybar Equation Yields Same Prediction at Every X Value. Lots of Error with this Model. Ybar = $370,058.95 (PLOT CHART WITH YBAR AND SALES) Yhat Equation Yields Predictions that are MUCH Closer to Sample Points. Much Less Error with this Model. Yhat = $8.24*x + 36,857 (PLOT CHART WITH YHAT AND SALES (X)) Positive Residuals 1 63,566 651,334 560,739 90,595 8.2415488163 2 50,762 527,670 454,184 73,486 3 50,941 523,751 455,052 68,699 4 17,597 175,467 182,701 -7,234 5 33,029 377,978 308,555 69,423 6 58,543 520,100 516,272 3,828 7 60,492 620,856 532,118 88,738 8 59,686 593,739 524,140 69,599 189 32,779 211,928 173,775 38,154 190 49,959 401,212 180,313 220,899 Plot Est. Line Plot Ybar x Predicted Line x Ybar 14,591 14,591 64,717 64,717 i th Sample Point Weekly $ Ad Expense (x) Weekly $ Sales (y) Predicted = ŷ i = b 1 *X i +b 0 Residual (Y i - ŷi) Residual² = (Y i - ŷi)² Note 1: ΣY i = Σŷ i Note 2: Σe i = 0 Lots of Error with this Model. Ybar = $370,058.95 Much Less Error with this Model. Yhat = $8.24*x + 36,857 ith Sample Point Weekly $ Ad Expense (x) Weekly $ Sales (y) Predicted = ŷi = b1*Xi+b0 Residual² = (Yi - ŷi)²
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ý = $8.24*Xi + $36857.04 Residuals = Distance from Particular Y value to Predicted Value. Estimated Equation can sometimes Overpredict or Underpredict . 10 K 0 K 100 K 200 K 300 K 400 K 500 K 600 K 700 K Weekly $ Sales (y)
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TREND FORMULA 560739.327936968 560739.328004162 455214.536893103 455214.536923111 456689.77413122 456689.774161748 181883.570400617 181883.570334306 309067.151733711 309067.151712217 519342.028232709 519342.028285315 535404.806875672 535404.806933938 528762.118529736 528762.118585662 307006.764529636 307006.764507417 448596.573193617 448596.573221293 Slope 8.2415488192 8.2415488163 Intercept 36857.0357628232 36857.0358802413 Negative Residuals Ybar Deviations Ybar Positive Error Ybar Negative Error If we use just Ybar for making predictions, we would not have a very good Model.
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