To analyze the relationship between the hours slept (x) and the corresponding test scores (y), we can first set up the data points from the table you provided.
Here's the data in a more visual format:
| Hours Slept (x) | Test Score (y) | |------------------|-----------------| | 4 | 62 | | 6 | 75 | | 6 | 88 | | 8 | 79 | | 10 | 97 |
Now, we'll input this data into a regression calculator to generate a scatterplot along with a trend line. However, as I cannot create visualizations directly, I will walk you through how it can be determined.
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Scatterplot Creation:
- Plot the points (4, 62), (6, 75), (6, 88), (8, 79), and (10, 97) on a graph.
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Trend Line:
- Using a regression analysis, you can obtain a linear equation in the form of \(y = mx + b\). The slope \(m\) and y-intercept \(b\) will describe how test scores change as a function of the number of hours slept.
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Prediction for 5 Hours Sleep:
- Assuming you get the linear regression equation from your calculation, plug \(x = 5\) into the equation to predict the test score \(y\).
Actuarial Point Based on Provided Data:
Since I do not have actual regression output, I can infer based on the values you've provided:
Estimated Values:
- Since there are no data points for exactly 5 hours, we can estimate based on the surrounding values.
- For 4 hours (62) and 6 hours (75 surprisingly lower than the trend we might expect).
- A simple estimate could suggest that the score after sleeping for 5 hours will likely fall between 62 and 75.
Conclusion:
- As the number of hours sleeping increases, the corresponding test score appears to increase generally. Therefore, I expect the score after sleeping for 5 hours to be around the range of 70 (you can use linear interpolation to get a more precise figure if actual output was available).
To get the precise score, please compute the linear regression using a calculator or plotting software available to you.