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Start by making a scatter plot.
Scatter Plot:
Correlation Coefficient: Close to 1
Prediction: 85.3
The table shown below represents the relation between the number of books read and the students' grades.
| Books | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 2 | 2 | 3 | 5 | 8 | 10 | 14 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Grade | 64 | 68 | 69 | 72 | 71 | 74 | 76 | 75 | 79 | 85 | 86 | 91 | 94 | 99 | 98 |
In order to find an equation for the line of fit, we will make a scatter plot. Let x represent the number of books and y represent the grade.
Substitute ( 0,72) & ( 14,99)
Subtract terms
Calculate quotient
Round to 1 decimal place(s)
Thus, the slope for the line o fit is 1.9. y=1.9x+ b Next, we will determine the y-intercept. Since the line passes through the point (0,72), we can immediately determine the y-intercept as 72. Thus, we can write the equation as the following. y=1.9x+72 When we examine the scatter plot, we notice that points lie closely to the line and we also know that the slope of the line 1.9 is positive. Thus, there is a strong positive correlation and the correlation coefficient is close to 1. Now, let's predict the grade of a student who read 7 books.
Our prediction of the grade of the student is 85.3.