Chapter 2A - Solution Manual

Chapter 2A - Solution Manual - Chapter 02A Least-Squares...

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Chapter 02 A Least-Squares Regression Computations Appendix 2A Least-Squares Regression Computations Exercise 2A-1  (20 minutes) 1. Month Rental Returns  (X) Car Wash Costs  (Y) January. .......... 2,310 $10,113 February. ........ 2,453 $12,691 March. ............. 2,641 $10,905 April. ............... 2,874 $12,949 May. ................ 3,540 $15,334 June. ............... 4,861 $21,455 July. ................ 5,432 $21,270 August. ............ 5,268 $19,930 September. ..... 4,628 $21,860 October. .......... 3,720 $18,383 November. ...... 2,106   $9,830 December. ...... 2,495 $11,081 The least-squares regression results are as follows: Intercept (fixed cost). .................. $2,296 Slope (variable cost per unit). ..... $3.74 R 2 ............................................... 0.92 Therefore, the cost formula is $2,296 per month plus $3.74 per  rental return or: Y = $2,296 + $3.74X Note that the R 2  is 0.92, which means that 92% of the variation in  glazing costs is explained by the number of units glazed. This is a  very high R 2  and indicates a very good fit. 2A-1
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Chapter 02 A Least-Squares Regression Computations Exercise 2A-1  (continued) While not a requirement of the exercise, it is always a good to plot the  data on a scattergraph. The scattergraph can help spot nonlinearities  or other problems with the data. In this case, the regression line  (shown below) is a reasonably good approximation to the relationship  between car wash costs and rental returns. 2A-2
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Chapter 02 A Least-Squares Regression Computations 2A-3
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Chapter 02 A Least-Squares Regression Computations Exercise 2A-2  (30 minutes) 1. Week Units  (X) Total Glazing Cost  (Y) 1 8 $270 2 5 $200 3 10 $310 4 4 $190 5 6 $240 6 9 $290 The least-squares regression results are as follows: Intercept (fixed cost). .................. $107.50 Slope (variable cost per unit). ..... $20.36 R 2 ............................................... 0.98 Therefore, the cost formula is $107.50 per week plus $20.36 per  unit or: Y = $107.50 + $20.36X Note that the R 2  is 0.98, which means that 98% of the variation in  glazing costs is explained by the number of units glazed. This is a  very high R 2  and indicates a very good fit. 2. Y = $107.50 + $20.36X 3. Total expected glazing cost if 7 units are processed: Variable cost: 7 units × $20.36 per unit. .................. $142.52 Fixed cost. ...............................................................   107.50     Total expected cost. ................................................ $250.02 2A-4
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Chapter 02 A Least-Squares Regression Computations Problem 2A-3  (45 minutes) 1.
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Chapter 2A - Solution Manual - Chapter 02A Least-Squares...

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