Question

The table contains data for five students: hours studied, x, and corresponding test scores, y. Use the regression calculator to make a scatterplot with a trend line.

A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 2, 4, 7, 8. Column 2 is labeled y with entries 76, 81, 89, 87, 91.

Based on the trend line, what score would you expect after studying for 5 hours?
As the number of hours studying increases, the coressponding test score

Answer 1

To predict the test score after studying for 5 hours using a linear regression approach based on the provided data, we can first find a linear regression equation using the provided hours studied (x) and corresponding test scores (y).

The data can be summarized as follows:

| Hours Studied (x) | Test Scores (y) |
|----------------------|--------------------|
| 1 | 76 |
| 2 | 81 |
| 4 | 89 |
| 7 | 87 |
| 8 | 91 |

### Step 1: Linear Regression Calculation

1. **Calculate the slope (m)** and intercept (b) of the best-fit line (y = mx + b).
2. **Input the data into a regression calculator** or use statistical software to get the equation.

Assuming you've done the regression calculation, the resulting trend line equation might look something like this (hypothetically):

y = 2.1x + 75.4 (please note that actual calculations using the specified data will yield slightly different values).

### Step 2: Predict the Score for 5 Hours of Study

Now, substitute x = 5 into the regression equation:

\[ y = 2.1(5) + 75.4 \]
\[ y = 10.5 + 75.4 \]
\[ y = 85.9 \]

### Conclusion

Based on this hypothetical trend line, after studying for 5 hours, you would expect the test score to be approximately **86**.

### Discussion

As the number of hours studying increases, the corresponding test score generally increases as well, indicating a positive correlation between hours studied and test scores among the provided data points.