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, yˆ=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 statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Summation Table x y xyxy x2x2 y2y2 Bid 1 2323 11 2323 529529 11 Bid 2 2424 22 4848 576576 44 Bid 3 3232 66 192192 10241024 3636 Bid 4 3737 99 333333 13691369 8181 Bid 5 4949 1010 490490 24012401 100100 Sum 165165 2828 10861086 58995899 222222 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 yˆ.
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, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price.
Keep in mind, the
Summation Table
| x | y | xyxy | x2x2 | y2y2 | |
|---|---|---|---|---|---|
| Bid 1 | 2323 | 11 | 2323 | 529529 | 11 |
| Bid 2 | 2424 | 22 | 4848 | 576576 | 44 |
| Bid 3 | 3232 | 66 | 192192 | 10241024 | 3636 |
| Bid 4 | 3737 | 99 | 333333 | 13691369 | 8181 |
| Bid 5 | 4949 | 1010 | 490490 | 24012401 | 100100 |
| Sum | 165165 | 2828 | 10861086 | 58995899 | 222222 |
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 yˆ.
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