Consider the following data: A women’s clothing department wants to find out if there is a relationship (and what kind of relationship) between the price of an item and the time that it takes to a customer to decide in buying that item. Item Price (x) Decision Time (in minutes) (Y) $30 12 $20 8 $300 37 $80 20 $78 15 $25 10 $17 9 $63 14 $150 20 $250 30 $10 4 $8 5 $180 27 $260 28 Give (or calculate) the regression equation coefficients; Give the equation of regression. Based on the above values, in detail draw the conclusion: Discuss the correlation coefficient r Discuss the coefficient of determination r2 Discuss in detail the meaning of the regression equation
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.
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Consider the following data:
A women’s clothing department wants to find out if there is a relationship (and what kind of relationship) between the price of an item and the time that it takes to a customer to decide in buying that item.
|
Item Price (x) |
Decision Time (in minutes) (Y) |
|
$30 |
12 |
|
$20 |
8 |
|
$300 |
37 |
|
$80 |
20 |
|
$78 |
15 |
|
$25 |
10 |
|
$17 |
9 |
|
$63 |
14 |
|
$150 |
20 |
|
$250 |
30 |
|
$10 |
4 |
|
$8 |
5 |
|
$180 |
27 |
|
$260 |
28 |
- Give (or calculate) the regression equation coefficients; Give the equation of regression.
Based on the above values, in detail draw the conclusion:
- Discuss the
correlation coefficient r - Discuss the coefficient of determination r2
- Discuss in detail the meaning of the regression equation
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