I have collected real data on the sale of a microwavable cup of soup across 20 different cities for the same time period (a month).  The variables in the dataset are:   Quantity sold in the city for that month:  Measured in thousands of units Price:  measured in dollars Average Income in the city:  Measured in thousands of dollars Ads:  Average number of ads run in stores for that city during that month. Price of a substitute product:  measured in dollars Population of the city:  measured in thousands of people   The dataset is on Canvas and, using Excel or any other statistical software, please answer the following questions:   1. Describe the patterns in quantity sold and own and rival prices during this time period using basic descriptive statistics.  Graphs are welcome as well.   2. Take the logs of the variables, and estimate the demand function. a. Interpret the R-square. b. Interpret the coefficients for logP and logPsub c. Interpret the p-values associated with each independent variable   3. Are consumers price sensitive?  Why or why not?  (be as precise as you can – you have estimates!). Does this price sensitivity make sense given the good we are examining?   4. How sensitive are our consumers to changes in the rival good’s price?  Explain in detail.   5. Suppose we decide to charge a per ounce price of $2, while at the same time our rival charges a price of $2.15.  All else equal, what would you expect sales to be?  How confident are you in your forecast?  Explain.   6. Suppose we are charging a price of $2 and our currentmarginal cost is $1.50  Are we maximizing profits at this price?  If not, should we raise or lower price?  Why?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 5PPS
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I have collected real data on the sale of a microwavable cup of soup across 20 different cities for the same time period (a month).  The variables in the dataset are:

 

Quantity sold in the city for that month:  Measured in thousands of units

Price:  measured in dollars

Average Income in the city:  Measured in thousands of dollars

Ads:  Average number of ads run in stores for that city during that month.

Price of a substitute product:  measured in dollars

Population of the city:  measured in thousands of people

 

The dataset is on Canvas and, using Excel or any other statistical software, please answer the following questions:

 

1. Describe the patterns in quantity sold and own and rival prices during this time period using basic descriptive statistics.  Graphs are welcome as well.
 
2. Take the logs of the variables, and estimate the demand function.
a. Interpret the R-square.
b. Interpret the coefficients for logP and logPsub
c. Interpret the p-values associated with each independent variable
 
3. Are consumers price sensitive?  Why or why not?  (be as precise as you can – you have estimates!). Does this price sensitivity make sense given the good we are examining?
 
4. How sensitive are our consumers to changes in the rival good’s price?  Explain in detail.
 
5. Suppose we decide to charge a per ounce price of $2, while at the same time our rival charges a price of $2.15.  All else equal, what would you expect sales to be?  How confident are you in your forecast?  Explain.
 
6. Suppose we are charging a price of $2 and our currentmarginal cost is $1.50  Are we maximizing profits at this price?  If not, should we raise or lower price?  Why?
### City Data Statistics Table

This table presents various statistical data points across 20 different cities, indicated by numerical identifiers (1 through 20). Each city is evaluated across six different metrics, labelled as Q, P, I, A, Psub, and Pop. Below is a detailed description of each column in the dataset:

1. **City**: Numerical identifier for each city.
2. **Q**: A quantitative measure for the city.
3. **P**: Another quantitative measure.
4. **I**: An index value attributed to the city.
5. **A**: A specific attribute associated with the city.
6. **Psub**: A subsequent measure related to P.
7. **Pop**: The population size of the city, expressed in some unit (likely thousands or millions).

Here are the first five rows as an example:

| City | Q    | P   | I    | A    | Psub | Pop  |
|------|------|-----|------|------|------|------|
| 1    | 32.92| 1.89| 32.4 | 4.38 | 2.08 | 98.7 |
| 2    | 28.51| 1.94| 29.9 | 4.12 | 2.06 | 104.5|
| 3    | 33.94| 1.99| 29.1 | 5.06 | 2.15 | 105.1|
| 4    | 33.45| 2.04| 28.6 | 5.36 | 2.18 | 106.9|
| 5    | 35.68| 2.09| 30.2 | 5.38 | 2.18 | 108.9|

### Summary and Analysis

- **Q** ranges from 20.84 to 45.74.
- **P** values span from 1.89 to 2.09.
- **I** measurements range from 23.8 to 32.4.
- **A** has values between 3.39 and 6.43.
- **Psub** ranges from 1.98 to 2.39.
- **Pop** (population) spans from 98.7 to 150.1.

Such a dataset can be
Transcribed Image Text:### City Data Statistics Table This table presents various statistical data points across 20 different cities, indicated by numerical identifiers (1 through 20). Each city is evaluated across six different metrics, labelled as Q, P, I, A, Psub, and Pop. Below is a detailed description of each column in the dataset: 1. **City**: Numerical identifier for each city. 2. **Q**: A quantitative measure for the city. 3. **P**: Another quantitative measure. 4. **I**: An index value attributed to the city. 5. **A**: A specific attribute associated with the city. 6. **Psub**: A subsequent measure related to P. 7. **Pop**: The population size of the city, expressed in some unit (likely thousands or millions). Here are the first five rows as an example: | City | Q | P | I | A | Psub | Pop | |------|------|-----|------|------|------|------| | 1 | 32.92| 1.89| 32.4 | 4.38 | 2.08 | 98.7 | | 2 | 28.51| 1.94| 29.9 | 4.12 | 2.06 | 104.5| | 3 | 33.94| 1.99| 29.1 | 5.06 | 2.15 | 105.1| | 4 | 33.45| 2.04| 28.6 | 5.36 | 2.18 | 106.9| | 5 | 35.68| 2.09| 30.2 | 5.38 | 2.18 | 108.9| ### Summary and Analysis - **Q** ranges from 20.84 to 45.74. - **P** values span from 1.89 to 2.09. - **I** measurements range from 23.8 to 32.4. - **A** has values between 3.39 and 6.43. - **Psub** ranges from 1.98 to 2.39. - **Pop** (population) spans from 98.7 to 150.1. Such a dataset can be
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5. Suppose we decide to charge a per ounce price of $2, while at the same time our rival charges a price of $2.15.  All else equal, what would you expect sales to be?  How confident are you in your forecast?  How do you get P=0.07 in the solution

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