Question

Read the scenario given below. With your group, examine the data set (on page 2) and decide what analysis should be done. Perform this analysis. Record your results and submit this file on Blackboard by the end of the day. Each student must submit a copy of their results.

Scenario:

Students are often late to class. This is distracting to both students and teachers, and is quite annoying. The school and instructors realize that some students have long commutes, but do not think that should affect the students’ ability to be on time to class. So the question was asked, “Do the students who have longer commutes tend to come to class later?”

Analysis:

1. Rewrite this question from a statistical standpoint. Use appropriate statistical language.

2. Find any values that will help you answer this question.

3. Interpret your results in the context of the problem.

4. Find the linear model that best predicts how late a student will be to class based on his/her commute. Type the equation for that model here.

5. Create a scatter plot with a trendline in Excel. Copy and paste the graph here.

6. If a particular student has a 9 minute commute, predict how late he/she will be to class.

7. A student travelling 9 minutes to school is 12 minutes late. Does the model from our data over- or under-predict how late the student is?

8. An instructor wants to use this model to predict how late students might be based on their self-reported commute times. What are some problems you might see with using this model? Explain why you might not recommend using it using appropriate statistical justification.

Data:

Commute Time	Average # of Minutes Late to Class
25	13
10	20
16	11
36	17
40	6
15	18
23	14
18	20
8	13
21	12
40	15
24	15
19	18
13	20
55	17
27	12
31	13
34	3
45	4
12	18
30	1
42	9
28	11
14	17

Answer 1

Sol:

Question according to Statistical standpoint is how average minutes late to class is related to commute time?

or how is the average minutes late is related to commute time?

SUMMARY OUTPUT Regression Statistics Multiple R 0.473346261 R Square 0.224056683 Adjusted R Square 0.188786532 Standard Error 4.889958348 Observations 24 ANOVA SS MSF Significance F 0 .019476941 6.352586469 Regression Residual Total 72 151.9010952 151.9011 526.0572382 23.91169 677.9583333 Intercept X Variable 1 Coefficients 18.62533718 -0.207680659 Standard Errort Stat 2.369711056 7.85975 0.082398776 -2.52043 P-value 7.90784E-08 0.019476941 Lower 95% 13.71085727 -0.37856526 Upper 95% 2 3.5398171 -0.036796057

Regression equation will be

y(hat)= -0.21x+18.63

Coefficient of determination or R squarred is 0.224 which indicates that the model explains 22.4% of the variability of the response data around its mean.

Correlation coefficient= -0.473 ( Negative association)

Interpretation of slope coefficient = The coefficient indicates that for every additional unit minute commute you can expect to there is 0.21 minutes late for the class, intercept remains constant.

If x= 9 minutes

y(hat)= -0.21*9+18.63= 16.74 minutes late for class.

A student travelling 9 minutes to school is 12 minutes late. The model under-predict. As per the equation the student will 16.74 approximately 17 minutes late.

y=-0.207x + 18.62 R? = 0.224 - Linear (y) 20 30 40 50

Since R squarred is very small , we can not recommend this model. Also the points are not close to lines they are highly scattered.