ABC Company has decided to use 20 test markets to examine the sensitivity of demand for its new product, Hand Sanitizer, to various prices, as shown in the following table. Each market had approximately the same level of business activity and population. Test Market Quantity sold (Thousands of Pens) Price Charged (cent) 1 20 50 2 21 50 3 19 55 4 18 60 5 20 60 6 14 65 7 16 65 8 20 70 9 12 70 10 14 80 11 12 70 12 10 70 13 14 65 14 16 90 15 18 45 16 16 70 17 20 65 18 12 80 19 18 70 20 10 50 Q.1. Using a linear regression model, estimate the demand function for ABC Company’s new product, Hand sanitizer. Q.2. Interpret the coefficient value of the independent variable of the estimated demand function. Q.3. What will be the predicted/estimated sale for each price shown in column 2?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
ABC Company has decided to use 20 test markets to examine the sensitivity of demand for its new product, Hand Sanitizer, to various prices, as shown in the following table. Each market had approximately the same level of business activity and population.
|
Test Market |
Quantity sold (Thousands of Pens) |
Price Charged (cent) |
|
1 |
20 |
50 |
|
2 |
21 |
50 |
|
3 |
19 |
55 |
|
4 |
18 |
60 |
|
5 |
20 |
60 |
|
6 |
14 |
65 |
|
7 |
16 |
65 |
|
8 |
20 |
70 |
|
9 |
12 |
70 |
|
10 |
14 |
80 |
|
11 |
12 |
70 |
|
12 |
10 |
70 |
|
13 |
14 |
65 |
|
14 |
16 |
90 |
|
15 |
18 |
45 |
|
16 |
16 |
70 |
|
17 |
20 |
65 |
|
18 |
12 |
80 |
|
19 |
18 |
70 |
|
20 |
10 |
50 |
Q.1. Using a linear regression model, estimate the demand
Q.2. Interpret the coefficient value of the independent variable of the estimated demand function.
Q.3. What will be the predicted/estimated sale for each price shown in column 2?
Q.4. Find the prediction interval at 95% for price of 70 cent.
Q.5. Interpret your prediction interval of Q.4.
Q.6. Conduct the hypothesis test at k=0.5:
(a) Set the null and alternative hypothesis
(b) Calculate standard deviation of the errors to calculate t-statistic
(c) Calculate t-statistic
(d) Find the critical value at k=.05 using the t-distribution table
(e) State the decision rule and apply your critical value to test the hypothesis
(f) Draw conclusion of your hypothesis test.
Q.7. Calculate the
Q.8. Find the value of coefficient of determination (r2).
Q.9. Interpret the coefficient of determination.
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