# ANOVA and Least Squares Regression

For the purposes of this session long project, I tracked my driving time to work on a daily basis for 15 days. During this 15 day period, I took the same route to work and left my house at 6:45 every morning. The total driving distance from my residence to my office is 5.5 miles, and the speed limit for the majority of the route is 45 miles per hour. During this period, I drove the speed limit and only slowed or stopped for stop signs, traffic signals, slower moving traffic, and school buses. For this study, I have converted all times into seconds to simplify calculations. The below chart is the data collected over this time period and reasons for any delays.

DATE DRIVING TIME SECONDS MEMO

6-Nov-12 12 min 19 Sec 739 No lights or buses

7-Nov-12 13 min 08 sec 788 Stop light for 39 sec

8-Nov-12 14 min 41 sec 881 2 Buses followed

9-Nov-12 11 min 33 sec 693 No lights or buses

13-Nov-12 12 min 12 sec 732 No lights or buses

14-Nov-12 13 min 11 sec 791 1 bus followed

15-Nov-12 15 min 56 sec 956 1 bus and long line at gate

16-Nov-12 11 min 38 sec 698 No lights or buses

19-Nov-12 12 min 20 sec 640 Stop light for 44 sec

20-Nov-12 12 min 37 sec 757 No lights or buses

30 Nov 12 11 min 51 sec 711 No lights or buses

3-Dec-12 16 min 54 sec 1014 1 school bus and random vehicle inspection at base main gate

4-Dec-12 14 min 12 sec 852 1 bus and long line at gate

5-Dec-12 12 min 34 sec 754 No lights or buses

6-Dec-12 12 min 03 sec 723 No lights or buses

TASKS:

1. Divide your data in half, the first 8 observations and the last 7 observations. Then use ANOVA to test to see if there is a significant difference between the two halves of your data.

2. Take the data and arrange it in the order it is collected. Count the total number of observations, and label this number N. Then create another set of data starting from one and increasing by one until you reach N. For example, if you have 10 observations, then your new set of data would be (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). This set of data is called a time series. Run a regression using the original set of data as the dependent variable, and the time series as an independent variable. Use the simple regression calculation page to calculate the regression. Write a response reporting the results and any conclusions that can be reached with it.

#### Solution Preview

Hi,

Please find the solution of your posting. I hope it will help you to understand the topic. Thanks!

SOLUTION:

1) Here is the data:

First Half Second Half

739 640

788 757

881 711

693 1014

732 852

791 754

956 723

698

Null Hypothesis (Ho): There is no significant difference in the population mean seconds between the two halves of the data.

Alternative Hypothesis (Ha): There ...

#### Solution Summary

This solution is comprised of a detailed explanation for Analysis of variance and least square regression. A data is divided in such a way so that the ANOVA can be performed on the given data. Full description is given including, Null and Alternative Hypotheses, level of significance, ANOVA table, P-value, F-value, decision about rejecting or not rejecting the null hypothesis along with concluding remarks are given in the solution. ANOVA output is generated using excel add ins "Data Analysis".