Homework SourseJoe Smith is considering opening a franchise of a very popul
Joe Smith is considering opening a franchise of a very popular gourmet fruit drink store. He is interested in constructing a multiple regression model to predict the number of drinks sold in a day based upon the volume of foot traffic passing the store, the daily maximum temperature and the average drink price.
Information has been collected on 30 randomly selected days for several randomly chosen stores: show data
Download the data
a)Find the multiple regression equation using all three explanatory variables. Assume that x1 is volume of traffic, x2 is maximum daily temperature and x3 is average drink price. Give your answers to 3 decimal places.
y^ = + vol. traffic + max temp + average drink price
b)At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis isis not rejected.
c)The value of R2 for this model, to 2 decimal places, is equal to
d)The value of s for this model, to 3 decimal places, is equal to
e)The least significant explanatory variable in this model is:
vol. traffic
max temp
average drink price
f)Construct a new multiple regression model by removing the variable average drink price. Give your answers to 3 decimal places.
The new regression model equation is:
y^ = + vol. traffic + max temp
g)In the new model compared to the previous one, the value of R2 (to 2 decimal places) is:
increased
decreased
unchanged
h)In the new model compared to the previous one, the value of s (to 3 decimal places) is:
increased
decreased
unchanged
i)The better model is the:
original model
reduced model
| Number of drinks sold | Volume of traffic (people per day) | Daily max temp °F | Average drink price |
|---|---|---|---|
| 690 | 413 | 65 | 2.3 |
| 870 | 442 | 108 | 3.65 |
| 499 | 240 | 104 | 3.15 |
| 726 | 311 | 108 | 3.4 |
| 773 | 437 | 108 | 2.85 |
| 571 | 388 | 85 | 3.5 |
| 519 | 276 | 74 | 1.8 |
| 470 | 209 | 107 | 2.2 |
| 507 | 251 | 109 | 2.65 |
| 753 | 404 | 94 | 2.55 |
| 737 | 363 | 107 | 3.15 |
| 373 | 182 | 63 | 2.25 |
| 733 | 333 | 110 | 3.45 |
| 718 | 407 | 68 | 2.45 |
| 692 | 315 | 95 | 3.05 |
| 479 | 201 | 80 | 2.95 |
| 701 | 443 | 65 | 2.15 |
| 931 | 499 | 94 | 2 |
| 684 | 367 | 70 | 2.05 |
| 845 | 490 | 95 | 2.95 |
| 807 | 453 | 61 | 1.65 |
| 887 | 441 | 103 | 3.6 |
| 893 | 480 | 105 | 3.9 |
| 710 | 453 | 66 | 2.3 |
| 523 | 207 | 94 | 2.55 |
| 730 | 349 | 108 | 3.35 |
| 678 | 324 | 93 | 4 |
| 482 | 303 | 86 | 3.75 |
| 541 | 187 | 113 | 2.45 |
| 872 | 498 | 110 | 2.1 |
Solution
a)Find the multiple regression equation using all three explanatory variables. Assume that x1 is volume of traffic, x2 is maximum daily temperature and x3 is average drink price. Give your answers to 3 decimal places.
Regression Analysis
R²
0.876
Adjusted R²
0.862
n
30
R
0.936
k
3
Std. Error
55.902
Dep. Var.
drinks sold
ANOVA table
Source
SS
df
MS
F
p-value
Regression
576,403.0553
3
192,134.3518
61.48
6.15E-12
Residual
81,249.7447
26
3,124.9902
Total
657,652.8000
29
Regression output
confidence interval
variables
coefficients
std. error
t (df=26)
p-value
95% lower
95% upper
Intercept
-24.6411
71.0638
-0.347
.7316
-170.7148
121.4326
traffic
1.3666
0.1032
13.246
4.55E-13
1.1545
1.5786
temp
2.5556
0.6932
3.687
.0011
1.1308
3.9804
price
-5.5324
18.1444
-0.305
.7629
-42.8287
31.7640
y^ = + vol. traffic + max temp + average drink price
y^ = -24.641 + 1.367*vol. traffic + 2.556*max temp - 5.532*average drink price
b)At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis is rejected.
c)The value of R2 for this model, to 2 decimal places, is equal to 0.88
d)The value of s for this model, to 3 decimal places, is equal to 55.902
e)The least significant explanatory variable in this model is:
vol. traffic
max temp
average drink price
f)Construct a new multiple regression model by removing the variable average drink price. Give your answers to 3 decimal places.
Regression Analysis
R²
0.876
Adjusted R²
0.867
n
30
R
0.936
k
2
Std. Error
54.955
Dep. Var.
drinks sold
ANOVA table
Source
SS
df
MS
F
p-value
Regression
576,112.5299
2
288,056.2649
95.38
5.76E-13
Residual
81,540.2701
27
3,020.0100
Total
657,652.8000
29
Regression output
confidence interval
variables
coefficients
std. error
t (df=27)
p-value
95% lower
95% upper
Intercept
-29.7264
67.9088
-0.438
.6651
-169.0636
109.6109
traffic
1.3650
0.1013
13.476
1.67E-13
1.1572
1.5729
temp
2.4477
0.5860
4.177
.0003
1.2454
3.6500
The new regression model equation is:
y^ = + vol. traffic + max temp
y^ = -29.726+ 1.365*vol. traffic +2.448* max temp
g)In the new model compared to the previous one, the value of R2 (to 2 decimal places) is: 0.88
increased
decreased
unchanged
h)In the new model compared to the previous one, the value of s (to 3 decimal places) is: 54.955
increased
decreased
unchanged
i)The better model is the:
original model
reduced model
| Regression Analysis | ||||||
| R² | 0.876 | |||||
| Adjusted R² | 0.862 | n | 30 | |||
| R | 0.936 | k | 3 | |||
| Std. Error | 55.902 | Dep. Var. | drinks sold | |||
| ANOVA table | ||||||
| Source | SS | df | MS | F | p-value | |
| Regression | 576,403.0553 | 3 | 192,134.3518 | 61.48 | 6.15E-12 | |
| Residual | 81,249.7447 | 26 | 3,124.9902 | |||
| Total | 657,652.8000 | 29 | ||||
| Regression output | confidence interval | |||||
| variables | coefficients | std. error | t (df=26) | p-value | 95% lower | 95% upper |
| Intercept | -24.6411 | 71.0638 | -0.347 | .7316 | -170.7148 | 121.4326 |
| traffic | 1.3666 | 0.1032 | 13.246 | 4.55E-13 | 1.1545 | 1.5786 |
| temp | 2.5556 | 0.6932 | 3.687 | .0011 | 1.1308 | 3.9804 |
| price | -5.5324 | 18.1444 | -0.305 | .7629 | -42.8287 | 31.7640 |
