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Measurements for Supervisors Utilizing Microsoft ® Exceed expectations 4 th Version Part 13 Prologue to Numerous Relapse The Different Relapse Model Thought: Look at the direct relationship between 1 subordinate (Y) and 2 or more free variables (X i )

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Insights for Managers Using Microsoft Â® Excel 4 th Edition Chapter 13 Introduction to Multiple Regression Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

The Multiple Regression Model Idea: Examine the direct relationship between 1 subordinate (Y) & 2 or more free variables (X i ) Multiple Regression Model with k Independent Variables: Population inclines Random Error Y-catch Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Multiple Regression Equation The numerous\' coefficients relapse model are assessed utilizing example information Multiple relapse comparison with k autonomous variables: Estimated (or anticipated) estimation of Y Estimated capture Estimated incline coefficients In this section we will dependably utilize Excel to acquire the relapse slant coefficients and other relapse rundown measures. Measurements for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Multiple Regression Equation (proceeded with) Two variable model Y Slope for variable X 1 X 2 Slope for variable X 2 X 1 Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Example: 2 Independent Variables A merchant of solidified desert pies needs to assess elements thought to impact request Dependent variable: Pie deals (units every week) Independent variables: Price (in $) Advertising ($100âs) Data are gathered for 15 weeks Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Pie Sales Example Multiple relapse mathematical statement: Sales = b 0 + b 1 (Price) + b 2 (Advertising) Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Estimating a Multiple Linear Regression Equation Excel will be utilized to produce the coefficients and measures of decency of fit for various relapse Excel: Tools/Data Analysis... /Regression Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Multiple Regression Output Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

The Multiple Regression Equation where Sales is in number of pies every week Price is in $ Advertising is in $100âs. b 1 = - 24.975 : deals will diminish, by and large, by 24.975 pies for each week for each $1 increment in offering cost, net of the impacts of changes because of publicizing b 2 = 74.131 : deals will increment, by and large, by 74.131 pies for every week for each $100 increment in promoting, net of the impacts of changes because of value Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Using The Equation to Make Predictions Predict deals for a week in which the offering cost is $5.50 and publicizing is $350: Note that Advertising is in $100âs so $350 implies that X 2 = 3.5 Predicted deals is 428.62 pies Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Coefficient of Multiple Determination Reports the extent of aggregate variety in Y clarified by all X variables taken together Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Multiple Coefficient of Determination (proceeded with) 52.1% of the variety in pie deals is clarified by the variety in value and publicizing Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Adjusted r 2 r 2 never diminishes when another X variable is added to the model This can be a burden when looking at models What is the net impact of including another variable? We lose a level of opportunity when another X variable is included Did the new X variable add enough logical energy to balance the loss of one level of flexibility? Measurements for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Adjusted r 2 (proceeded with) Shows the extent of variety in Y clarified by all X variables balanced for the quantity of X variables utilized (where n = test size, k = number of autonomous variables) Penalize intemperate utilization of irrelevant free variables Smaller than r 2 Useful in contrasting among models Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Adjusted r 2 (proceeded with) 44.2% of the variety in pie deals is clarified by the variety in value and publicizing, considering the specimen size and number of free variables Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Simple and Multiple Regression Compared Coefficients in a straightforward relapse get the effect of that variable in addition to the effects of different variables that are corresponded with it and the subordinate variable. Coefficients in a numerous relapse net out the effects of different variables in the comparison. Insights for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Simple and Multiple Regression Compared:Example Two basic relapses: ABSENCES= a + b 1 AUTONOMY ABSENCES= a + b 2 SKILLVARIETY Multiple Regression: ABSENCES= a + b 1 AUTONOMY+ b 2 SKILLVARIETY Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Venn Diagrams and Regression Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Venn Diagrams and Regression Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Overlap in Explanation Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Is the Model Significant? F-Test for Overall Significance of the Model Shows if there is a direct relationship between the X\'s majority variables considered together and Y Use F test measurement Hypotheses: H 0 : Î² 1 = Î² 2 = â¦ = Î² k = 0 (no straight relationship) H 1 : no less than one Î² i â 0 (no less than one free variable influences Y) Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

F-Test for Overall Significance Test measurement: where F has (numerator) = k and (denominator) = (n â k - 1) degrees of flexibility Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

F-Test for Overall Significance (proceeded) With 2 and 12 degrees of flexibility P-esteem for the F-Test Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

H 0 : Î² 1 = Î² 2 = 0 H 1 : Î² 1 and Î² 2 not both zero ï¡ = .05 df 1 = 2 df 2 = 12 F-Test for Overall Significance (proceeded with) Test Statistic: Decision: Conclusion: Critical Value: F ï¡ = 3.885 Since F test measurement is in the dismissal locale (p-esteem < .05), reject H 0 ï¡ = .05 0 F There is confirmation that no less than one autonomous variable influences Y Do not dismiss H 0 Reject H 0 F .05 = 3.885 Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Are Individual Variables Significant? Use t-tests of individual variable inclines Shows if there is a direct relationship between the variable X i and Y Hypotheses: H 0 : Î² i = 0 (no straight relationship) H 1 : Î² i â 0 (straight relationship does exist between X i and Y) Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Are Individual Variables Significant? (proceeded with) H 0 : Î² i = 0 (no direct relationship) H 1 : Î² i â 0 (straight relationship does exist between x i and y) Test Statistic: ( df = n â k â 1) Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Are Individual Variables Significant? (proceeded with) t-esteem for Price is t = - 2.306, with p-esteem .0398 t-esteem for Advertising is t = 2.855, with p-esteem .0145 Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

H 0 : Î² i = 0 H 1 : Î² i ï¹ 0 Inferences about the Slope: t Test Example From Excel yield: d.f. = 15-2-1 = 12 = .05 t ï¡/2 = 2.1788 The test measurement for every variable falls in the dismissal district (p-values < .05) Decision: Conclusion: Reject H 0 for every variable a/2=.025 a/2=.025 There is proof that both Price and Advertising influence pie deals at ï¡ = .05 Reject H 0 Do not dismiss H 0 Reject H 0 - t Î±/2 t Î±/2 0 - 2.1788 Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Job Earnings Example http://www.ilir.uiuc.edu/courses/lir593/jearnoutput.htm ERTEN: 27.4/2.5= 10.9 t 1171 UNEM: - 229.1/45.9= - 5.0 t 1171 EDU: 885.13/76.5= 11.6 t 1171 Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Confidence Interval Estimate for the Slope Confidence interim for the populace incline Î² i where t has (n â k â 1) d.f. Here, t has (15 â 2 â 1) = 12 d.f. Case: Form a 95% certainty interim for the impact of changes in value (X 1 ) on pie deals: - 24.975 Â± (2.1788)(10.832) So the interim is (- 48.576 , - 1.374) Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Confidence Interval Estimate for the Slope (proceeded with) Confidence interim for the populace slant Î² i Example: Excel yield likewise reports these interim endpoints: Weekly deals are evaluated to be lessened by between 1.37 to 48.58 pies for every increment of $1 in the offering value Statistics for Managers Using Microsoft Excel, 4e Â© 2004 Prentice-Hall, Inc.

Qualitative Independent Var