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 109 113 155 167 170 Number of Bids 10 11 12 13 17 Summation Table X Y XY X2 Y2 BID 1 109 10 1090 11881 100 BID 2 113 11 1243 12769 121 BID 3 155 12 1860 24025 144 BID 4 167 13 2171 27889 169 BID 5 170 17 2890 28900 289 SUM 714 63 9254 105464 823 Step 1: Find the estimated slope. Step 2: Find the estimated y-intercept. Step 3: Find the estimate value of y when x=113. Step 4: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false. 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
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 | 109 | 113 | 155 | 167 | 170 |
| Number of Bids | 10 | 11 | 12 | 13 | 17 |
Summation Table
| X | Y | XY | X2 | Y2 | |
| BID 1 | 109 | 10 | 1090 | 11881 | 100 |
| BID 2 | 113 | 11 | 1243 | 12769 | 121 |
| BID 3 | 155 | 12 | 1860 | 24025 | 144 |
| BID 4 | 167 | 13 | 2171 | 27889 | 169 |
| BID 5 | 170 | 17 | 2890 | 28900 | 289 |
| SUM | 714 | 63 | 9254 | 105464 | 823 |
Step 1: Find the estimated slope.
Step 2: Find the estimated y-intercept.
Step 3: Find the estimate value of y when x=113.
Step 4: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.
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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