Standard Error

     2.  A 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 this new drug called XBC 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 (thousands of   dollars), x Number of Orders, y   1 68.93 2,902,000   2 72.62 3,893,000   3 79.58 3,299,000   4 58.67 2,130,000   5 69.18 3,367,000   6 70.14 4,111,000   7 93.37 4,923,000   8 78.88 4,935,000   9 92.99 5,276,000   10 75.23 3,654,000   11 91.38 5,598,000   12 52.9 2,967,000   13 61.27 2,999,000   14 89.19 4,345,000   15 90.03 4,934,000   16 78.21 3,653,000   17 83.77 5,625,000   18 82.53 5,978,000   19 98.76 5,999,000   20 92.64 5,834,000    

     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.    

     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 Analysis to   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 4,999,000. (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.    

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