Step 1: Calculate the sum of squared errors. Use the values b0= -9.7658 and b1=0.5868 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 80% confidence interval for the slope. Step 5: Construct the 90% confidence interval for the slope.
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 | 21 | 22 | 22 | 23 | 31 |
| Number of Bids | 1 | 3 | 3 | 6 | 8 |
Summation Table
| X | Y | XY | X2 | Y2 | |
| Item 1 | 21 | 1 | 21 | 441 | 1 |
| Item 2 | 22 | 3 | 66 | 484 | 9 |
| Item 3 | 22 | 3 | 66 | 484 | 9 |
| Item 4 | 23 | 6 | 138 | 529 | 36 |
| Item 5 | 31 | 8 | 248 | 961 | 64 |
| SUM | 119 | 21 | 539 | 2899 | 119 |
Step 1: Calculate the sum of squared errors. Use the values b0= -9.7658 and b1=0.5868 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 80% confidence interval for the slope.
Step 5: Construct the 90% confidence interval for the slope.
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