Question

Pizza Hut is facing stiff competition in it pizza delivery service, and you are the owner who is particularly concerned about being able to provide call-in customers with a guarantee as to how quickly their pizza would arrive. You have collected a month’s worth of data that included travel time (y)/ minute and delivery distance (x)/miles. You want to know if you can use delivery distance to predict travel time. You run regression on excel, and get the following output. Answer questions following the output.

1). Using the knowledge you learned from Chapter 3 to summarize Travel time and Delivery distance. What is the characteristics of this sample?

2). Determine the least-squares regression equation for travel time as a function of distance. Interpret the slope.

3). What percentage of the variation in travel time(y) is explained by the delivery distance (x)?

4). Do hypothesis testing to test the significance of slope and follow the 4-step. What does it tell you about the relationship between pizza delivery distance and travel time? (α=0.05)

5. what is the 95% confidence interval for slope? How does it tell you about the significance of the slope? Does this conclusion agree with the conclusion from 4)?

6).What would be the estimated time of travel for a pizza delivery that involved 5-miles? Interpret the result.

7). Calculate the prediction interval for the individual travel time given a pizza delivery distance is 5 miles (Show your calculation details in Excel). Interpret the results. (α=0.05)

8). Calculate the confidence interval for the mean of travel time given a pizza delivery distance is 5 miles (Show your calculation details in Excel). Interpret the results. (α=0.05)

9). Comparing results from 7) and 8), which one is wider? Why?

10). Calculate SSR, SSE and SST for this model.

Travel_Time
6.02
5.47
8.99
7.98
9.01
10.86
6.31
7.87
12.47
7.58
10.65
7.83
6.75
9.59
6.99
8.94
8.38
5.62
5.67
9.18
5.04
8.16
6.81
3.71
6.44
7.98
5.85
4.72
7
8.52
8.48
6.61
8.98
7.93
10.31
4.86
8.9
8.78
6.27
8.83
7.54
10.49
8.33
7.76
8.88
7.17
8.98
7.06
9.86
5.71
7.12
6.08
7.91
6.05
5.91
7.53
6.31
7.37
4.27
7.87
7.11
7.28
9.83
6.28
5.83
5.5
8.89
7.08
5.57
7.83
7.74
11.29
8.72
6.31
9.69
10.02
11.41
5.87
6.64
9.65
10.88
6.43
6.71
4.12
8.88
5.86
10.74
5.83
8.25
6.93
7.81
9.33
6.04
5.6
7.04
9.41
10.93
8.14
6.46
7.79
7.06
4.27
8.87
10.19
8.14
7.91
8.28
4.85
8.02
9.36
8.52
7.35
7.59
8.33
11.22
5.97
8.28
6.63
9.56
6.7
5.83
6.02
6.47
8.16
6.55
7.17
8.62
8.81
9.62
9.39
4.88
9.21
5.18
9.17
7.78
10.49
4.91
8.54
4.07
5.88
7.09
5.8
7.03
7.94
8.45
6.59
10.75
8.68
6.05
8.3
8.53
5.96
8.2
5.67
8.85
9.02
6.65
10.36
7.9
8.51
7.73
9.24
9.91
5.85
4.68
8.47
9.02
10.57
10.71
3.52
10.56
5.09
8.47
6.81
10.84
6.47
7.33
8.82
9.34
8.24
7.54
9.43
11.21
10.67
7.7
6.37
8.14
8.22
9.41
6.62
4.83
6.55
3.12
7.19
9.39
6.9
8.29
11.85
8.83
3.92
12.25
9.9
8.68
8.97
9.56
8.65
10.49
6.87
4.86
11.14
8.76
9.41
3.93
9.98
6.32
9.4
6.54
8.45
5.3
6.96
6.88
8.22
8.06
12.55
9
8.25
12.58
9.63
10.42
7.69
7.88
7.43
6.56
4.72
8.58
8.83
7.65
12.43
6.09
7.79

  

Distance
2.5
3.3
4.9
3.8
4.9
5.3
2.9
3.5
6.4
3.5
5.1
3.7
3.6
5.2
3.4
4.8
3.7
2.4
3.1
4.4
2.2
3.8
3.5
1.7
2.5
4.1
2
1.9
3.6
3.6
3.9
3.3
4.4
3.9
4.8
2.1
4.7
4.6
3.3
3.7
3.6
5.8
4.2
3.6
4
4
4.4
3.8
4.9
2.8
4
3.1
4
3.3
2.7
4.1
3.3
3.9
2.1
4.4
3.8
3.5
4.8
2.9
3
2.9
4.3
3.8
2.8
4.4
3.4
5.3
3.9
3.5
4.9
4.9
5.7
2.9
3.2
5.2
5
3.2
2.9
2.2
4.6
2.7
6.1
2.4
3.4
3.8
3.9
5
3.2
3
3.2
4.9
5.1
4.1
3.2
3.9
3.1
2.3
4.5
4.9
4.8
4.5
4.7
2.5
3.7
5.6
3.8
2.7
4
3.8
5.9
2.6
4.2
3
4.9
3.8
2.6
3
2.6
4.3
3.9
3.4
4.3
4.2
4.6
4.6
2.5
4.7
2
4.7
4.3
5.1
2.4
4.3
1.2
3.7
3.5
2.6
3.4
3.9
4
2.8
5.4
3.6
3
4.2
3.7
2.7
3.2
3.2
4.6
4.5
3.5
5.1
4.4
4.3
4.1
4.3
5.1
2.4
3.1
4.6
4.9
5.2
5.2
1.9
5.8
2.7
4.2
3.4
5.5
3.4
3.5
4.6
4.3
3.9
4.1
5.2
5.5
5.9
3.7
2.8
3.7
3.8
4
3.1
3
3.2
1.7
3.3
5
2.9
3.7
5.8
4.6
2.3
5.5
5.3
4.1
4
4.7
4.6
5.3
3
2.5
6.1
4.6
4.4
2.5
4.2
3.3
4.5
3.3
4.2
2.5
3.6
2.9
4.7
4.1
6.4
4.7
4.1
6.4
5
5
3.8
4
3.6
3.1
2.9
4.9
5.1
4
5.4
2.7
4

Answer 1

1.

Travel time and distance are continuous bivariate observations.

2.