The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, Y=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in dollars 31 38 42 44 46 Number of Bids 3 4 6 7 9 Summation Table X Y XY X2 Y2 BID 1 31 3 93 961 9 BID 2 38 4 152 1444 16 BID 3 42 6 252 1764 36 BID 4 44 7 308 1936 49 BID 5 46 9 414 2116 81 SUM 201 29 1219 8221 191 Step 1: Find the estimated slope. Step 2: Find the estimated y-intercept. Step 3: Determine the value of the dependent variable Y at x=0. Step 4: Find the estimate value of y when x=42. Step 5: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable y. Step 6: Find the value of the coefficient of determination.
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 table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, Y=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the
| Price in dollars | 31 | 38 | 42 | 44 | 46 |
| Number of Bids | 3 | 4 | 6 | 7 | 9 |
Summation Table
| X | Y | XY | X2 | Y2 | |
| BID 1 | 31 | 3 | 93 | 961 | 9 |
| BID 2 | 38 | 4 | 152 | 1444 | 16 |
| BID 3 | 42 | 6 | 252 | 1764 | 36 |
| BID 4 | 44 | 7 | 308 | 1936 | 49 |
| BID 5 | 46 | 9 | 414 | 2116 | 81 |
| SUM | 201 | 29 | 1219 | 8221 | 191 |
Step 1: Find the estimated slope.
Step 2: Find the estimated y-intercept.
Step 3: Determine the value of the dependent variable Y at x=0.
Step 4: Find the estimate value of y when x=42.
Step 5: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable y.
Step 6: Find the value of the coefficient of determination.
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