1. A heating contractor sends a repair person to homes in response to calls about heating problems. The contractor would like to have a way to estimate how long the 32 customer will have to wait before the repair person can begin work. Data on the number of minutes of waiting time (Wait Time) and the backlog of previous calls waiting for service (Backlog) were obtained. The data table is listed. Answer the questions below. You may use MINITAB (or, possibly another program) for answering these questions.

(a) Find the linear regression equation resulting from regression of WaitTime on Backlog. Give an interpretation for the slope and the intercept.

(b) Calculate the predicted value and the 95% prediction interval for the time to respond to a call when the backlog is 6.

(c) Consider a regression for a model with the base-10 logarithm of Wait Time as a response and Backlog as a predictor. Run a linear regression in Minitab for this model. Does this model appear better than the one without taking the logarithm of the Wait Time?

(d) Calculate the predicted value for the log of the Wait Time when the backlog is 6.

(e) Convert your answer to question (d) to a predicted value for the Wait Time when the backlog is 6.

Wait Tim	Backlog
220	4
230	1
60	1
280	2
210	2
40	0
470	3
540	4
40	0
60	3
80	2
90	3
50	3
30	0
70	3
20	1
140	1
30	0
70	1
100	3
10	2
40	3
10	1
140	3
120	4
30	2
370	2
90	2
450	3
10	0
100	4
130	1
50	2
40	1
10	1
70	2
360	4
40	2
30	0
180	1
20	2
210	2
40	0
40	0
40	1
60	1
30	0
10	0
30	1
40	1
80	3
60	1
30	3
10	2
280	3
130	2
30	3
70	3
130	1
250	3
100	3
260	4

2. The data below contains driving accuracy (y) and driving distance (x) of various golf players. We use the driving distance here as a predictor, and driving accuracy as a response. Use MINITAB (or another software, if you wish) to answer the questions below.

(a) Find a 95% prediction interval for the driving accuracy if the driving distance is x = 300 yards.

(b) Find a 95% confidence interval for the average value of the driving accuracy if the driving distance is x = 300 yards.

(c) Compare the intervals in parts (a) and (b). Which interval is wider? Is this always the case?

PLAYER	DISTANCE	ACCURACY	INDEX
Woods	316.1	54.6	3.58
Perry	304.7	63.4	3.48
Gutschewski	310.5	57.9	3.27
Wetterich	311.7	56.6	3.18
Hearn	295.2	68.5	2.82
Gronberg	301.4	63.2	2.74
Frazar	301	63.5	2.74
Warren	299.2	64.2	2.55
Glover	302.2	60.7	2.27
MacKenzie	300.2	62.1	2.22
Love III	305.4	57.9	2.21
Garcia	303.5	59.4	2.21
Durant	289.2	70.9	2.2
O'Hair	300.1	61.4	2.02
Singh	301.1	60.2	1.92
Long	298.3	62.4	1.9
Smith	300.8	60.2	1.85
Hend	318.9	45.4	1.89
Hughes	291.3	67.5	1.76
Stadler	300.1	60.4	1.76
Allenby	297.7	62.3	1.75
Mayfair	288.2	69.8	1.71
Appleby	300.6	59.3	1.58
Snyder III	291.8	66.3	1.56
Purdy	295.2	63.4	1.52
Brigman	295.5	63.1	1.5
Bryant	283.2	73	1.49
Rollins	294.4	63.7	1.43
Jobe	302.3	57.3	1.42
Brehaut	286.6	69.9	1.4
Ogilvy	298	60.7	1.4
Henry	297.6	61	1.4
Rose	294.1	63.7	1.37
Westwood	296.8	61.5	1.36
Johnson	290	66.9	1.34
Senden	291	66	1.31
Mickelson	300	58.7	1.3
Watney	298.9	59.4	1.26
Trahan	295.8	61.8	1.23
Pappas	309.4	50.6	1.17

3. The file below has the following columns that are relevant to this exercise: SalesPerSF: Sales per square foot of stores operated by a retail chain, 33 Income: the median household income in the surrounding community (dollars), Population000: and the size of the community (in thousands). Market: This is a qualitative variable. There are 3 types of geographic locations: urban, suburban, and rural. Two dummy variables have been set up, UrbanDummy and SuburbanDummy. Rural is selected as the base level. Disregard the other columns in the file.

(a) Run a regression using SalesPerSF as the dependent variable, and Income, Population000, and the two dummy variables as predictors. Which of the coefficients are significantly different from zero?

(b) Predict the sales per square foot for a store located in a suburban community with median household income $71,000, and population size equal to 500,000 people. Write a 95% prediction interval and a 95% confidence interval. Explain the difference between the two intervals.

(c) Interpret all four coefficients in the estimated regression equation.

SalesPerSF	Income	Population000	Market	UrbanDummy	SuburbanDummy	UrbanTimesIncome	SuburbanTimesIncome
544.3	89000	503	Urban	1	0	89000	0
481.2	78000	463	Urban	1	0	78000	0
527.5	71000	597	Urban	1	0	71000	0
550.5	64000	452	Urban	1	0	64000	0
561.1	69000	684	Urban	1	0	69000	0
491.1	59000	610	Urban	1	0	59000	0
691.7	76000	699	Urban	1	0	76000	0
483.5	59000	663	Urban	1	0	59000	0
572.6	64000	760	Urban	1	0	64000	0
582	76000	569	Urban	1	0	76000	0
403.3	61000	685	Urban	1	0	61000	0
612.8	73000	872	Urban	1	0	73000	0
489.1	68000	712	Urban	1	0	68000	0
481	84000	514	Urban	1	0	84000	0
441.5	78000	326	Urban	1	0	78000	0
573.8	76000	769	Urban	1	0	76000	0
467.9	78000	421	Urban	1	0	78000	0
607.6	72000	499	Urban	1	0	72000	0
508.9	67000	672	Urban	1	0	67000	0
587.4	71000	1077	Urban	1	0	71000	0
393.4	65000	710	Urban	1	0	65000	0
564.2	52000	592	Urban	1	0	52000	0
588.3	72000	829	Urban	1	0	72000	0
569.4	73000	650	Urban	1	0	73000	0
641.9	88000	755	Urban	1	0	88000	0
646.4	78000	531	Urban	1	0	78000	0
490.1	67000	559	Urban	1	0	67000	0
616.5	69000	726	Urban	1	0	69000	0
467.1	61000	581	Urban	1	0	61000	0
630.2	79000	531	Urban	1	0	79000	0
532.9	75000	470	Urban	1	0	75000	0
353.2	52000	551	Urban	1	0	52000	0
580.2	71000	482	Urban	1	0	71000	0
379.3	86000	849	Suburban	0	1	0	86000
495.8	84000	796	Suburban	0	1	0	84000
468.4	86000	713	Suburban	0	1	0	86000
362.9	80000	578	Suburban	0	1	0	80000
355.8	73000	798	Suburban	0	1	0	73000
455.9	74000	786	Suburban	0	1	0	74000
382	84000	740	Suburban	0	1	0	84000
476.2	87000	850	Suburban	0	1	0	87000
376.8	85000	828	Suburban	0	1	0	85000
341.4	77000	729	Suburban	0	1	0	77000
428	70000	926	Suburban	0	1	0	70000
465.5	90000	641	Suburban	0	1	0	90000
475.7	80000	953	Suburban	0	1	0	80000
442	74000	862	Suburban	0	1	0	74000
469.3	86000	1224	Suburban	0	1	0	86000
555.2	73000	992	Suburban	0	1	0	73000
401.7	71000	626	Suburban	0	1	0	71000
488.8	93000	947	Suburban	0	1	0	93000
512	71000	1075	Suburban	0	1	0	71000
437.9	95000	884	Suburban	0	1	0	95000
417.5	76000	1034	Suburban	0	1	0	76000
352.7	75000	827	Suburban	0	1	0	75000
416.7	73000	985	Suburban	0	1	0	73000
283.5	64000	635	Suburban	0	1	0	64000
454	92000	424	Suburban	0	1	0	92000
466.6	78000	923	Suburban	0	1	0	78000
461.1	79000	793	Suburban	0	1	0	79000
376	63000	612	Rural	0	0	0	0
162.8	50000	560	Rural	0	0	0	0
458.3	64000	452	Rural	0	0	0	0
325.7	58000	611	Rural	0	0	0	0
313.1	62000	433	Rural	0	0	0	0
305.1	54000	705	Rural	0	0	0	0
276.6	65000	658	Rural	0	0	0	0
310.5	65000	438	Rural	0	0	0	0
272.7	59000	434	Rural	0	0	0	0
425.6	70000	552	Rural	0	0	0	0
468.4	72000	656	Rural	0	0	0	0
209.4	62000	410	Rural	0	0	0	0
126.9	55000	321	Rural	0	0	0	0
325.9	74000	270	Rural	0	0	0	0
442.9	66000	738	Rural	0	0	0	0
458.2	69000	548	Rural	0	0	0	0
409.9	60000	774	Rural	0	0	0	0
349.2	56000	646	Rural	0	0	0	0
471.4	67000	831	Rural	0	0	0	0
476.4	56000	947	Rural	0	0	0	0
407.5	63000	945	Rural	0	0	0	0
375.1	66000	323	Rural	0	0	0	0
319.8	66000	260	Rural	0	0	0	0
287.2	56000	401	Rural	0	0	0	0
518.1	63000	628	Rural	0	0	0	0
213.8	63000	222	Rural	0	0	0	0
290.9	65000	395	Rural	0	0	0	0