The following data represents the number of Christmas Trees sold per day at a local Christmas Tree Farm and their prices. Price of Tree (x) Units/# of Trees Sold (y) 34 4 36 4 32 6 35 5 31 9 38 2 39 1 1. Compute the sample correlation coefficient between the price and the number of trees sold 2. Develop a least-squares estimated regression line 3. Compute the coefficient of determination and explain its meaning
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.
| The following data represents the number of Christmas Trees sold per day at a local Christmas Tree Farm and their prices. |
| Price of Tree (x) | Units/# of Trees Sold (y) |
| 34 | 4 |
| 36 | 4 |
| 32 | 6 |
| 35 | 5 |
| 31 | 9 |
| 38 | 2 |
| 39 | 1 |
1. Compute the sample
2. Develop a least-squares estimated regression line
3. Compute the coefficient of determination and explain its meaning
4. Test to see if x and y are significantly related. Use a significance level of α = 0.01.
-Test for Overall Significance using P-Value and Critical Value Methods
-Test for Individual Significance using P-Value and Critical Value Methods
*Excel can be used to solve this problem
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Regression:
The regression analysis is conducted here by using EXCEL. The software procedure is given below:
- Enter the data.
- Select Data > Data Analysis >Regression> OK.
- Enter Input Y Range as y
- Enter Input X Range as x
- Click OK.
The output using EXCEL is as follows:
Step by step
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