# Project #81196 - Simple Regression & Hypothesis Testing on Multiple Populations

Must be done in Excel **

A CEO of a large pharmaceutical company would like to determine if the company should be placing more money allotted in the budget next year for television advertising of a new drug marketed for controlling diabetes. He wonders whether there is a strong relationship between the amount of money spent on television advertising for this new drug called DIB and the number of orders received. The manufacturing process of this drug is very difficult and requires stability so the CEO would prefer to generate a stable number of orders. The cost of advertising is always an important consideration in the phase I roll-out of a new drug. Data that have been collected over the past 20 months indicate the amount of money spent of television advertising and the number of orders received.

The use of linear regression is a critical tool for a manager's decision-making ability. Please carefully read the example below and try to answer the questions in terms of the problem context. The results are as follows:

 Month Advertising cost # of orders 1 \$78,420.00 2,856,000 2 62,620 1,810,000 3 55,580 1,299,000 4 93,680 1,730,000 5 71,180 2,367,000 6 63,140 2,611,000 7 85,370 4,778,000 8 76,880 1,935,000 9 69,990 2,155,000 10 77,230 3,434,000 11 59,380 1,598,000 12 62,750 1,867,000 13 73,270 2,899,000 14 86,190 3,545,000 15 61,530 1,534,000 16 79,540 2,891,000 17 63,350 1,625,000 18 84,530 3,778,000 19 79,760 2,979,000 20 74,640 3,814,000

a. Set up a scatter diagram and calculate the associated correlation coefficient. Discuss how strong you think the relationship is between the amount of money spent on television advertising and the number of orders received. Please use the Correlation procedures within Excel under Tools > Data Analysis. The Scatterplot can more easily be generated using the Chart procedure.

NOTE: If you do not have the Data Analysis option under Tools you must install it. You need to go to Tools select Add-ins and then choose the 2 data toolpak options. It should take about a minute.

b. Assuming there is a statistically significant relationship, use the least squares method to find the regression equation to predict the advertising costs based on the number of orders received. Please use the regression procedure within Excel under Tools > Data Analysisto construct this equation.

c. Interpret the meaning of the slope, b1, in the regression equation.

d. Predict the monthly advertising cost when the number of orders is 2,300,000. (Hint: Be very careful with assigning the dependent variable for this problem)

e. Compute the coefficient of determination, r2, and interpret its meaning.

f. Compute the standard error of estimate, and interpret its meaning.

g. Do you think that the company should use these results from the regression to base any corporate decisions on?….explain fully.

Hypothesis Testing on Multiple Populations

Dr. Michaella Evans, a statistics professor at the University of Maryland University College, drives from her home to the school every weekday. She has three options to drive there. She can take the Beltway, or she can take a main highway with some traffic lights, or she can take the back road, which has no traffic lights but is a longer distance. Being as data-oriented as she is, she is interested to know if there is a difference in the time it takes to drive each route.

As an experiment she randomly selected the route on 21 different days and wrote down the time it took her for the round trip, getting to work in the morning and back home in the evening.  At the .01 significance level, can she conclude that there is a difference betweenthe driving times using the different routes?

Time (in minutes) it took to get to work and back using:

 Beltway Main highway Back road 87 80 88 93 82 80 91 90 81 88 92 96 99 77 95 83 75 73 90 69 79

You can check your critical value with the following table:

 Subject Business Due By (Pacific Time) 09/07/2015 06:00 pm
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