The table below gives the number of hours five randomly selected students spent studying and their corresponding midterm exam grades. 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. Hours Studying 0 1 2 3 4 Number of Bids 73 79 87 88 97 Summation Table X Y XY X2 Y2 Student 1 0 73 0 0 5329 Student 2 1 79 79 1 6241 Student 3 2 87 174 4 7569 Student 4 3 88 264 9 7744 Student 5 4 97 388 16 9409 SUM 10 424 905 30 36292 Step 1: Find the estimated slope. Step 2: Find the estimated y-intercept. Step 3: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false. Step 4: 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 5: Find the estimate value of y when x=2. 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 number of hours five randomly selected students spent studying and their corresponding midterm exam grades. 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
| Hours Studying | 0 | 1 | 2 | 3 | 4 |
| Number of Bids | 73 | 79 | 87 | 88 | 97 |
Summation Table
| X | Y | XY | X2 | Y2 | |
| Student 1 | 0 | 73 | 0 | 0 | 5329 |
| Student 2 | 1 | 79 | 79 | 1 | 6241 |
| Student 3 | 2 | 87 | 174 | 4 | 7569 |
| Student 4 | 3 | 88 | 264 | 9 | 7744 |
| Student 5 | 4 | 97 | 388 | 16 | 9409 |
| SUM | 10 | 424 | 905 | 30 | 36292 |
Step 1: Find the estimated slope.
Step 2: Find the estimated y-intercept.
Step 3: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.
Step 4: 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 5: Find the estimate value of y when x=2.
Step 6: Find the value of the coefficient of determination.
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