1 / 62

Multiple Regression Analysis: Heating Oil Sales Prediction

Learn how to analyze heating oil sales using multiple regression with temperature and insulation as independent variables. Understand coefficient interpretation, categorical variables, hypothesis testing, significance, and factors affecting sales. Dive into ANOVA and hypothesis testing for car accidents.

raymond-sheppard
Télécharger la présentation

Multiple Regression Analysis: Heating Oil Sales Prediction

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Exam Feb 28: sets 1,2 • Set 1 due Thurs • Memo C-1 due Feb 14 • Free tutoring will be available next week Plan A: MW 4-6PM OR Plan B: TT 2-4PM VOTE for Plan A or Plan B Announce results Thurs

  2. Kinderman Supplement • Ch 2: Multiple Regression • Ch 3: Analysis of Variance

  3. MULTIPLE REGRESSION Kinderman, Ch 2

  4. Example • Reference: Statistics for Managers • By Levine, David M; Berenson; Stephan • Second edition (1999) • Prentice Hall

  5. Y = dependent variable = heating oil sales (gal) • X1 = Temperature (degrees) • X2 = Insulation (inches) • X1 and X2 are independent variables • Y = bo + b1X1 + b2X2 • Enter data to Excel • NOTE: If you can’t find Data Analysis, try Add-Ins

  6. Y = 562 –5X1 –20X2 Bottom table: Coefficient Column

  7. Interpret coefficients Intercept = bo = 562: If temp =0 and insulation = 0, heating oil sales = 562 • b1 = -5: For all homes with same insulation, each 1 degree increase in temperature should decrease heating oil sales by 5 gallons • b2 = -20: For all months with same temp, each additional 1 inch of insulation should decrease sales by 20 gallons

  8. Categorical Variables • X = 0 or 1 • Example: 0 if male, 1 if female • Example: 1 if graduate, 0 if drop out • Example: 1 if citizen, 0 if alien • NOTE: not in this fuel oil example

  9. Estimate sales if temp = 30, insulation = 6 • Y = 562 -5(30) – 20(6) = 292 gal

  10. Standard Error = 26Top table • Interpret: Typical fuel oil sales were about 26 gal away from average fuel oil sales of other homes with same temp and insulation

  11. COEFFICIENT OF MULTIPLEDETERMINATION • Top table, R square • Interpret: 96% of total variation in fuel oil sales can be explained by variation in temperature and insulation

  12. Is there a relationship between all independent variables and dependent variables? • Ho: Null hypothesis: All coefficients = 0 Ho: NO Relationship H1: Alternative hypothesis: At least one coefficient is not zero H1: There is a relationship

  13. Computer output: Sample data • Hypotheses: Population parameters • Ho: Parameters = 0, but sample data makes it appear that there is a relationship • Simple regression: Ho: zero slope vs H1: slope positive or slope negative

  14. Exponents • 10-1= 0.1 • 10-2 =0.01

  15. Decision Rule • Reject Ho if “Significance F” < alpha • Middle table • Fuel oil example: Significance F = 1.6E-09 • Excel: E = Exponent • 1.6E-09 = 1.6*10-9 =0.0000000016 • Approaches zero as limit

  16. Significance F=p-value • Excel uses p-value only if t distribution • Significance F = probability F is greater than Sample F

  17. Assume alpha = .05 • Since 0 < .05, reject Ho • We conclude there IS a relationship between fuel oil sales and the independent variables

  18. Which independent variables seem to be important factors? • Ho: Temperature not important factor • H1: Temperature is important • Reject Ho if p-value < alpha • Bottom table: p-value column, X1 row • P-value = 1.6E-09, or zero • Reject Ho • Temp is important

  19. Insulation • Ho: insulation unimportant • H1: insulation important • P-value = 1.9E-06, or zero • Reject Ho • Insulation important

  20. Analysis of Variance (ANOVA) Kinderman, Ch 3

  21. X = number of auto accidents

  22. Hypothesis Testing • Ho: µ1 = µ2 = µ 3 • H1: Not all means are = • H1: There are differences among 3 populations • H1: Average number of accidents different depending on where you live

  23. This course: manual calculations • If you used computer software, you could have as many populations as needed • Homework, exam: 3 populations • Computer: 4 or more populations • Ex: Ethnic classifications at CSUN

  24. Sample Sizes • Column 1: n1 = number of drivers sampled from policyholders living in city = 3 • Column 2: n2 = sampled from suburban drivers = 3 • Col 3: n3 = sampled from rural = 3 • Number of rows of data • Kinderman example: Different sample sizes

  25. n = n1 + n2 + n3 n =3 + 3 + 3 = 9

  26. X = number of auto accidents

  27. Do not assume n1=3 on exam

  28. X = number of auto accidents

  29. Hypotheses • Ho: Differences in sample means due to chance, but no differences if ALL drivers were included (Prop 103) • H1: Population means are different because city drivers have more accidents

  30. Grand mean = 1.1

  31. SSB = Sum of Squares Between • Between 3 groups • Explained Variation • Here: Variation in number of accidents explained by where you live (city, suburb, rural) • If where you live did not affect accidents, we would expect SSB = 0 • Next slide: SSB formula

  32. X = number of auto accidents

  33. This example • SSB = 3(2-1.1)2+3(1-1.1)2 +3(.3-1.1)2 =4.2

  34. MSB = Mean Square Between • MSB = SSB/2 • Note: OK for this course, but bigger problems would have bigger denominator • MSB = 4.2/2 = 2.1

  35. SSE= Sum of Squared Error • Variation within group • Ex: Variation within group of city drivers • Unexplained variation • If every city driver had same number of accidents, we would expect SSE = 0 • Formula on next slide

  36. X = number of auto accidents

  37. (1-2)2 +(3-2)2 +(2-2)2 +(2-1)2 + (0-1)2 + (1-1)2 +(1-.3)2 + (0-.3)2 + (0-.3)2 =4.67

  38. MSE = Mean Square Error Mean Square Within Next slide is formula for this course. Bigger problems have bigger denominator

More Related