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# Correlation and r2's

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1. The MBA department is concerned that dual degree students may be receiving lower grades than the regular MBA students. Two independent random samples have been selected. 100 observations from population 1 (dual degree students) and 100 from population 2 (MBA students). The sample means obtained are X1(bar)=84 and X2(bar)=87. It is unknown from previous studies that the population variances are 4.0 and 5.0 respectively. Using a level of significance of .10, is there evidence that the dual degree students are receiving lower grades? Fully explain your answer

2. CEO of a large pharmaceutical company would like to determine if he should be placing more money allotted
in the budget next year for television advertising of a new drug marketed for controlling asthma. He wonders whether there is a strong relationship between the amount of money spent on television advertising for his new drug called XBC and the numbers 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 1 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 (thousands of dollars) Number of Orders
1 \$55.93 4,102,000
2 70.62 3,893,000
3 79.58 5,299,000
4 58.67 4,130,000
5 69.18 4,367,000
6 70.14 4,111,000
7 73.37 3,923,000
8 68.88 4,935,000
9 82.99 5,276,000
10 75.23 4,654,000
11 71.38 4,398,000
12 52.9 2,967,000
13 61.27 3,999,000
14 79.19 4,345,000
15 60.03 3,934,000
16 78.21 4,653,000
17 93.77 5,625,000
18 62.53 3,978,000
19 88.76 4,999,000
20 92.64 5,834,000

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. 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 Analysis to construct this equation Interpret the meaning of the slope, b1, in the regression equation.
Predict the monthly advertising cost when the number of orders is 4,999,000. (Hint: Be very careful with assigning the dependent variable for this problem)
Compute the coefficient of determination, r2, and interpret its meaning.
Compute the standard error of estimate, and interpret its meaning.