https://file.aiquickdraw.com/mathbot/file/1728875928392kjzck8fg.xlsx

A random sample of 100 students enrolled in statistics units in recent semesters at Macquarie University has been selected to study participation in lectures, measured as the number of polling quizzes answered, and academic performance. Some of the variables recorded for each student are listed below.
Variable Description:
subid - Subject ID
liveStream - either “True”, if the student mostly watched the lectures via the live-stream, or “False”, if the student mostly came to classes
numQuizzes - the number of polling quizzes answered
unitMark - the final unit mark

Report the value of the estimated slope [use at least 4dp]:

To estimate the slope, I'll first examine the data in your file and then perform a regression analysis with the relevant variables. Let’s analyze the relationship between the number of polling quizzes answered (`numQuizzes`) and the final unit mark (`unitMark`), as these two variables will allow us to determine the estimated slope in predicting `unitMark` from `numQuizzes`. 

I’ll proceed with the analysis and get back to you with the estimated slope value.The dataset includes four columns: `SubID`, `liveStream`, `numQuizzes`, and `unitMark`. To estimate the slope for predicting `unitMark` based on `numQuizzes`, I’ll run a simple linear regression using `numQuizzes` as the predictor variable and `unitMark` as the response variable.

Let’s perform this regression analysis to find the slope.The estimated slope for predicting `unitMark` based on `numQuizzes` is approximately **0.6990** (to four decimal places). This suggests that, on average, each additional quiz answered is associated with an increase of about 0.699 points in the final unit mark.

Would you like a more detailed explanation of the regression analysis or additional insights on interpreting this slope?

Here are five related questions you might find useful:
1. What does the intercept represent in this context?
2. How does the slope impact predictions about a student’s final mark?
3. How can we test if this slope is statistically significant?
4. What other variables might influence the final unit mark in addition to `numQuizzes`?
5. How would the analysis change if we considered `liveStream` as an additional predictor?

**Tip:** When interpreting a slope, remember that it reflects the expected change in the dependent variable (response) for each one-unit increase in the independent variable (predictor).

A random sample of 100 students enrolled in statistics units in recent semesters at Macquarie University has been selected to study participation in lectures, measured as the number of polling quizzes answered, and academic performance. Some of the variables recorded for each student are listed below.

This analysis examines the relationship between the number of quizzes answered and final unit marks in a sample of 100 students from Macquarie University. Using linear regression, we estimate that each additional quiz answered is associated with a 0.699 increase in the final unit mark. Suitable for students studying statistics or data science.

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