Question

The owner of Boston sports bar believes that, on average, her restaurant is busier on days when the Red Sox play an away game (a game played at another team’s stadium), but she wants to be sure before adding more staff. To test whether this is true, she takes a random sample of 50 days over the course of the baseball season and records the total daily revenue, along with whether the Red Sox were playing away that day (1 if yes, 0 if no). Using the data provided, perform a regression analysis to determine the effect of Red Sox away games on revenue. Be sure to include the residuals and residual plot in your analysis.

USE EXCEL PLEASE
5 Kezdőlap chegg 1 - Excel (A termékaktiválás nem sikerült) Nézet Mondja el, mit szeretne tenni..., Fail Beszúrás Lapelrendezés Képletek Adatok Véleményezés 11 A Calibri F D A -A Sortöréssel több sorba Cellaegyesítés AutoSzum Kitöltés T örlése Beillesztés Megosztás Ay Rendezés és Keresés és szúrés kijelölés Altalános 9-% 000 Szám A - - 28.8 Feltételes Formázás formázás táblázatként Sulusok Collastílusok Beszúrás Törlés Formátum - Cellák Igazitás Vágólap Betűtipus E4 X V for A B C D E 1 Red Sox away games (1-yes, O-no) F G H I L M N O P Q R S T U V Munka1 @ -- + 92%

Answer 1

Answer: ---- The regression equation is defined as, Date: ---28/4/2020 Y = Bo + B1X Where, dependent variable Y is the Daily Revenue ($) and independent variable X is the Red Sox away games (1 if yes, O if no) Now, the regression analysis is done in excel by following steps Step 1: Write the data values in excel. The screenshot is shown below, A Daily Red Sox away Revenue ($) games 1560 2918 2541 1757 1853 2295 2773 1234 Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

OME INSERT PAGE LAYOUT FORMULAS A ZA EH ! Data Analysis DATA REVIE Data Analysis Analysis Tools OK Cancel Help Histogram Moving Average Random Number Generation Rank and Percentile Regression Sampling t-Test: Paired Two Sample for Means t-Test: Two-Sample Assuming Equal Variances t-Test: Two-Sample Assuming Unequal Variances z-Test: Two Sample for Means Step 3: Select Input Y Range: 'Daily Revenue' column, Input X Range: 'Red Sox away games' column, tick mark on Residuals and Residual Plots then OK. The screenshot is shown below,

Daily Red Sox away 1 Revenue ($) games 1560 2918 Regression Input Input Y Range: ок SA$1:$A$51 Cancel Input X Range: $B$1:$B$51 Help Labels Confidence Level: Constant is Zero 95 % Output options O Output Range: O New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals MResidual Plots Line Fit Plots Normal Probability Normal Probability Plots The result is obtained. The screenshot is shown below,

B C D E F SUMMARY OUTPUT Regression Statistics 4 Multiple R 0.474566 5 R Square 0.225213 6 Adjusted R Square 0.209072 7 Standard Error 466.3179 8 Observations 10 ANOVA df 12 Regression 13 Residual 14 Total SS MS F gnificance F 1 3034013 3034013 13.95254 0.000498 48 10437716 217452.4 49 13471729 Coefficientsandard Err t Stat P-value Lower 95%Upper 95% 17 Intercept 1768.318 99.41932 17.78646 9.15E-23 1568.422 1968.214 18 Red Sox away games 496.2532 132.8546 3.73531 0.000498 229.1311 763.3754 The Residuals values are,

RESIDUAL OUTPUT Observation | Predicted Daily Revenue (5) Residuals 2264.5714 -704.5714 2264.5714 653.4286 2264.5714 276.4286 2264.5714 -507.5714 2264.5714 -411.5714 2264.5714 30.4286 2264.5714 508.4286 1768.3182 -534.3182 1768.3182 463.6818 2264.5714 -189.5714 1768.3182 -552.3182 1768.3182 -432.3182 2264.5714 -124.5714

1768.3182 429.6818 2264.5714 -294.5714 1768.3182 602.6818 2264.5714 -589.5714 1768.3182 396.6818 1768.3182 -755.3182 2264.5714 332.4286 1768.3182 -768.3182 1768.3182 130.6818 1768.3182 592.6818 1768.3182 -142.3182 1768.3182 -71.3182 1768.3182 -117.3182 1768.3182 -539.3182 2264.5714 224.4286

1768.3182 29.6818 2264.5714 -90.5714 2264.5714 478.4286 1768.3182 410.6818 2264.5714 -118.5714 2264.5714 -312.5714 1768.3182 704.6818 2264.5714 360.4286 2264.5714 551.4286 2264.5714 -717.5714 2264.5714 27.4286 2264.5714 87.4286 2264.5714 210.4286 1768.3182 -669.3182

2264.5714 690.4286 2264.5714 100.4286 2264.5714 -584.5714 1768.3182 669.6818 46 47 1768.3182 -400.3182 2264.5714 -352.5714 1768.3182 551.6818 2264.5714 466.4286 The Residual plot is,

Red Sox away games Residual Plot 1000 Residuals 0 0.2 0.4 0.6 0.8 -5003 -1000 Red Sox away games from the regression output summary, the regression equation is, Ý = 1768,31821496.2532 x X The effect of When Red Sox were playing away ( X = 1) û = 1768.3182 + 496.2532 x 1 = 2264.5714 Daily revenue is $ 2264.5714

When Red Sox were not playing away (X = 0) Y = 1768.3182 + 496.2532 x 0 = 1768.3182 Daily revenue is $ 1768.3182 There is difference of $496.2532 which is considerably big.