Consider the relationship between the number of bids an item on ebay received and the item's selling price. The following is a sample of 5 items sold through an auction. Price in dollars 120 154 163 179 180 Number of Bids 14 14 16 18 20 Summation Table X Y XY X2 Y2 Item 1 120 14 1680 14400 196 Item 2 154 14 2156 23716 196 Item 3 163 16 2608 26569 256 Item 4 179 18 3222 32041 324 Item 5 180 20 3600 32400 400 SUM 796 82 13266 129126 1372 Step 1: Calculate the sum of squared errors. Use the values b0=2.3745 and b1=0.0881 for the calculations. Step 2: Calculate the estimated variance of errors, s2e. Step 3: Calculate the estimated variance of slope s2b1.
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.
Consider the relationship between the number of bids an item on ebay received and the item's selling price. The following is a sample of 5 items sold through an auction.
| Price in dollars | 120 | 154 | 163 | 179 | 180 |
| Number of Bids | 14 | 14 | 16 | 18 | 20 |
Summation Table
| X | Y | XY | X2 | Y2 | |
| Item 1 | 120 | 14 | 1680 | 14400 | 196 |
| Item 2 | 154 | 14 | 2156 | 23716 | 196 |
| Item 3 | 163 | 16 | 2608 | 26569 | 256 |
| Item 4 | 179 | 18 | 3222 | 32041 | 324 |
| Item 5 | 180 | 20 | 3600 | 32400 | 400 |
| SUM | 796 | 82 | 13266 | 129126 | 1372 |
Step 1: Calculate the sum of squared errors. Use the values b0=2.3745 and b1=0.0881 for the calculations.
Step 2: Calculate the estimated variance of errors, s2e.
Step 3: Calculate the estimated variance of slope s2b1.
Step 4: Construct the 98% confidence interval for the slope.
Step 5: Construct the 90% confidence interval for the slope.
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