Rita Sharp, Director of Operations at the Farnsworth Museum of Industrial Arts,
ID: 3312725 • Letter: R
Question
Rita Sharp, Director of Operations at the Farnsworth Museum of Industrial Arts, has gathered weekly visitor data for the past year. Rita is interested in explaining why the number of visitors (NUMV) varies from week to week. Rita has data on two independent variables. The first is a dummy variable coded 1 for weeks when new items went on display and coded 0 for all other weeks (NITEM). The second is a variable for the price of an admissions ticket because part of the museum’s marketing strategy is to have weekly reduced-price admission promotions (TPRICE). The director asks you to generate a regression equation using these data. Use the data below:
(1) produce a regression model
(2) interpret the parameters
(3) access the goodness of fit of the model. In summarizing the findings, what should you tell the director?
DATA:
NUMV 933 1240 983 1129 758 927 1247 870 1140 1231 1038 1184 991 1059 1397 756 1098 1330 1129 774 847 1206 1340 1166 816 821 919 1214 1320 1161 1207 1246 1006 1198 1331 1101 1214 1172 1137 1172 1309 1051 1009 1072 1118 1106 1197 1091 895 803 997 822
NITEM 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0
TPRICE 5 5 5 5 5 5 5 5 3 2.5 3 5 5 3 5 5 3 2.5 5 5 5 3 5 5 5 5 5 5 2.5 5 5 5 5 2.5 5 5 5 3 5 3 5 5 5 5 2.5 5 5 5 5 5 5 5
Explanation / Answer
Result:
Rita Sharp, Director of Operations at the Farnsworth Museum of Industrial Arts, has gathered weekly visitor data for the past year. Rita is interested in explaining why the number of visitors (NUMV) varies from week to week. Rita has data on two independent variables. The first is a dummy variable coded 1 for weeks when new items went on display and coded 0 for all other weeks (NITEM). The second is a variable for the price of an admissions ticket because part of the museum’s marketing strategy is to have weekly reduced-price admission promotions (TPRICE). The director asks you to generate a regression equation using these data. Use the data below:
when new items went on display, the number of visitors increases by 234.8086.
when price of an admissions ticket increases by 1 unit, the number of visitors decreases by 80.1911.
(3) access the goodness of fit of the model. In summarizing the findings, what should you tell the director?
Calculated F=19.52, P=0.0000 which is < 0.05 level.
The model is significant.
We conclude that the number of visitors is significantly related to price of an admissions ticket and the week when new items went on display.
Regression Analysis
R²
0.443
Adjusted R²
0.421
n
52
R
0.666
k
2
Std. Error
129.780
Dep. Var.
NUMV
ANOVA table
Source
SS
df
MS
F
p-value
Regression
657,562.8461
2
328,781.4230
19.52
0.0000
Residual
825,299.3847
49
16,842.8446
Total
1,482,862.2308
51
Regression output
confidence interval
variables
coefficients
std. error
t (df=49)
p-value
95% lower
95% upper
Intercept
1,383.6557
88.4499
15.643
0.0000
1,205.9089
1,561.4026
NITEM
234.8086
42.5969
5.512
1.31E-06
149.2070
320.4102
TPRICE
-80.1911
19.6656
-4.078
.0002
-119.7106
-40.6715
Regression Analysis
R²
0.443
Adjusted R²
0.421
n
52
R
0.666
k
2
Std. Error
129.780
Dep. Var.
NUMV
ANOVA table
Source
SS
df
MS
F
p-value
Regression
657,562.8461
2
328,781.4230
19.52
0.0000
Residual
825,299.3847
49
16,842.8446
Total
1,482,862.2308
51
Regression output
confidence interval
variables
coefficients
std. error
t (df=49)
p-value
95% lower
95% upper
Intercept
1,383.6557
88.4499
15.643
0.0000
1,205.9089
1,561.4026
NITEM
234.8086
42.5969
5.512
1.31E-06
149.2070
320.4102
TPRICE
-80.1911
19.6656
-4.078
.0002
-119.7106
-40.6715
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