Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow. Advertising Expenditures Revenue 1 19 2 32 4 44 6 40 10 52 14 53 20 54
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow.
|
Advertising Expenditures |
Revenue |
|---|---|
|
1 |
19 |
|
2 |
32 |
|
4 |
44 |
|
6 |
40 |
|
10 |
52 |
|
14 |
53 |
|
20 |
54 |
![a. Let \( x \) equal advertising expenditures and \( y \) equal revenue. Use the method of least squares to develop a straight line approximation of the relationship between the two variables.
[Answer]
b. Test whether revenue and advertising expenditures are related at a 0.05 level of significance.
[Answer]
c. Prepare a residual plot of \( y - \hat{y} \) versus \( \hat{y} \). Use the result from part (a) to obtain the values of \( \hat{y} \).
[Answer]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2db74e8-3589-4bf7-a910-802ed190420d%2F83a5a76a-20fd-41c4-8fee-49a52bd137a4%2Fbbp341_processed.jpeg&w=3840&q=75)
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