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BUS$252$S16$ $
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NAME:$$
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TEST$#1$–$VERSION$1$
(also$put$you$name$on$the$back$of$the$last$sheet)$
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#1$Attached$is$an$Excel$spreadsheet$containing$the$regression$analysis$of$Sales$for$
twenty$firms.$$The$analysis$involves$three$models.$$Model$1$is$the$multivariate$
model$and$treats$Sales$as$a$function$of$Advertising$expense$and$Promotion$expense.$$
Models$2$and$3$are$univariate$models.$$Model$2$treats$Sales$as$a$function$of$
Advertising.$$Model$3$treats$the$Sales$as$a$function$of$Promotion.$$(Sales,$
Advertising,$and$Promotion$are$all$measured$in$dollars.)$
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#1.1$Is$Model$1$(i.e.,$the$multivariate$model)$logical?$$If$so,$why;$if$not,$why$not?$$
(5$points)$
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#1.2$Is$Model$2$(i.e.,$the$univariate$model$where$Alumni$Giving$Rate$is$a$function$of$
Graduation$Rate)$logical?$$If$so,$why;$if$not,$why$not?$(5$points)$
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#1.3$Is$Model$3$(i.e.,$the$univariate$model$where$Alumni$Giving$Rate$is$a$function$of$
StudentUFaculty$Ratio)$logical?$$If$so,$why;$if$not,$why$not?$(5$points)$
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#1.4$For$Model$1,$is$the$estimate$of$the$intercept$statistically$significantly$different$
from$zero$at$the$0.05$level?$$If$so,$why?$$If$not,$why$not?$(5$points)$
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1.5$For$Model$1,$are$both$of$the$Advertising$and$Promotion$estimates$statistically$
significantly$different$from$zero$at$the$0.05$level?$If$so,$why?$$If$not,$why$not?$$
(5$points)$
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1.6$For$Model$1,$are$both$of$the$Advertising$and$Promotion$estimates$statistically$
significantly$different$from$zero$at$the$0.01$level?$If$so,$why?$$If$not,$why$not?$$
(5$points)$
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#1.7$What$percentage$of$the$variance$in$Sales$is$accounted$for$by$Model$1?$$
(5$points)$
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#1.8$Is$multicollinearity$present$in$the$multivariate$analysis?$$(If$so,$why;$if$not,$why$
not?)$(5$points)$
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#1.9$Which$is$the$best$model$among$Model$1,$Model$2,$and$Model$3?$(10$points)$
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Best$model:$
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Reason$it$is$the$best$model:$
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#1.10$Suppose$the$budget$for$next$year$allocates$$1,000$to$Advertising$and$$1,000$
to$Promotion.$$What$is$the$forecasted$value$of$Sales$using$Model$1?$(5$points)$
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#1.11$The$forecasted$values$of$Sales$via$Model$2,$given$Advertising$is$$1,000,$is$
$197,347,$and$the$forecasted$value$of$Sales$via$Model$3,$given$Promotion$is$$1,000,$
is$$205,890.$$Which$of$the$three$forecasts$(i.e.,$from$Model$1,$Model$2,$and$Model$3)$
would$you$use$and$why$would$you$use$it?$(5$points)$
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#2$Suppose$we$are$manufacturing$a$particular$item$using$machines$made$by$two$
different$companies,$one$machine$made$by$Wilson,$Inc.$and$the$other$machine$made$
by$Smith,$Inc.$$Data$on$the$time$between$breakdowns$for$these$two$machines$and$
the$related$regression$analysis$are$presented$below.$
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#2.1$Is$the$Age$of$the$machine$relevant$to$the$time$between$breakdowns$(at$the$0.05$
level)?$$If$so,$why;$if$not,$why$not?$(5$points)$
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#2.2$Is$the$Model$of$the$machine$(i.e.,$Smith$or$Wilson)$relevant$to$the$time$between$
breakdowns$(at$the$0.05$level)?$$If$so,$why;$if$not,$why$not?$(5$points)$
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#3$Below$is$a$dataset$and$the$Excel$regression$setUup$window.$$The$data$are$the$
rates$of$return$on$Stocks,$Treasury$Bills,$and$Treasury$Bonds$for$the$years$2000$
through$2009.$$FillUin$the$top$panel$of$the$regression$setUup$window$to$configure$
Excel$to$regress$Stocks$on$TUBills$and$TUBonds.$$(5$points)$
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#4$Below$is$the$Excel$regression$analysis$for$a$multivariate$linear$model$where$the$
dependent$variable$is$the$Sales$Price$of$each$of$thirty$houses$and$the$independent$
variables$are$the$number$of$Bedrooms,$the$number$of$Bathrooms,$and$the$size$(in$
Square$Feet)$of$each$house.$
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#4.1$$What$percentage$of$the$variance$in$Sales$Price$is$accounted$for$by$the$
multivariate$linear$model?$$(5$points)$
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#4.2$Which$of$the$regression$parameters$are$statistically$significantly$different$from$
zero$at$the$.05$level,$and$why?$$(5$points)$
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#4.3$Which$of$the$regression$parameters$statistically$significantly$different$from$
zero$at$the$.01$level,$and$why?$$(5$points)$
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#5$Data$on$counter$sales,$driveUthru$sales,$and$net$profits$(all$in$millions$of$dollars)$
from$ten$franchises$of$a$fast$food$chain$were$collected$and$analyzed,$as$follows:$
franchise #
1
2
3
4
5
6
7
8
9
10
counter sales
8.4
3.3
5.8
10.0
4.7
7.7
4.5
8.6
5.9
6.3
sales in millions of dollars
drive-thru sales
7.7
4.5
8.4
7.8
2.4
4.8
2.5
3.4
2.0
4.1
net profit
1.5
0.8
1.2
1.4
0.2
0.8
0.6
1.3
0.4
0.6
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.87858406
R Square
0.77190994
Adjusted R Square
0.70674135
Standard Error
0.24191195
Observations
10
ANOVA
df
Regression
Residual
Total
Intercept
counter sales
drive-thru sales
2
7
9
SS
1.386350255
0.409649745
1.796
Coefficients
-0.21589662
0.08547343
0.11315334
Standard Error
0.26429842
0.043796911
0.038529012
MS
F
Significance F
0.693175128 11.8448161 0.00566725
0.058521392
t Stat
P-value
Lower 95% Upper 95%
-0.816866877 0.44091504 -0.84086263 0.40906938
1.951585698 0.09195252 -0.01808974 0.18903659
2.936834726 0.0218112 0.02204677 0.20425991
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What$is$the$managerial$implication$of$the$analysis$(at$the$0.05$level)?$(5$points)$
#6$An$analysis$of$demand$for$a$particular$product$as$a$function$of$price$yielded$the$
following$results.$$
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While$the$simple$regression$analysis$appears$to$be$reasonably$good,$what$
alternative$form$of$linear$regression$analysis$would$you$recommend,$and$why?$$$
(5$points)$
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