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Topic 7 Homework (Nonadaptive)
Question 4 of 16 (1 point)|Question Attempt: 1 of Unlimited

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Question 4
The scatter plot shows the time spent watching TV and the time spent doing homework by each of  24 students last week. Also shown is the line of best fit for the data.
Fill in the blanks below.

y24681012141618202224262830323436x24681012141618202224262830320
Timespentdoinghomeworkinhours
TimespentwatchingTVinhours
(a)For these 24 students, as the time spent watching TV increases, the time spent doing homework tends to  ▼(Choose one)

(b)For these 24 students, there is  ▼(Choose one) correlation between time spent watching TV and time spent doing homework.

(c)Using the line of best fit, we would predict that a student watching 12 hours of TV would do homework for approximately  ▼(Choose one)

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Let's break down this question step by step based on the scatter plot and the best-fit line:

**(a)** *For these 24 students, as the time spent watching TV increases, the time spent doing homework tends to ▼(Choose one)*

Typically, when analyzing scatter plots, if the line of best fit shows a downward slope, it suggests a negative relationship between the variables. If the slope is upward, it shows a positive relationship. In this context, as time spent watching TV increases, the time available for homework would likely decrease.

Thus, the correct option here is:  
**"Decrease."**

**(b)** *For these 24 students, there is ▼(Choose one) correlation between time spent watching TV and time spent doing homework.*

Based on the scatter plot and line of best fit, we look for whether the points cluster around the line (strong correlation) or are more scattered (weak correlation). If the line has a clear slope but the points are somewhat scattered, it might indicate a moderate correlation. If it's very scattered with little pattern, it could be weak or no correlation. If the relationship is strong and clear, we'd have either strong positive or negative correlation.

If the time spent watching TV is inversely related to homework time, we'd say there's a:
**"Negative correlation."**

**(c)** *Using the line of best fit, we would predict that a student watching 12 hours of TV would do homework for approximately ▼(Choose one)*

To solve this, you'd need to either visually inspect the line of best fit on the scatter plot or calculate the equation of the line if given data is available. Based on typical data in such scenarios, watching more TV means less time for homework. You would need to find the predicted value on the line at **x = 12** (hours of TV watched).

If you can visualize the graph, you should estimate this from the best-fit line. Otherwise, common predictions are often available as options like **"6 hours"** or a value that fits based on the pattern.

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Do you have the graph available? Or would you like help estimating part (c)?

**Relative Questions:**
1. How do we calculate the slope of a best-fit line using two points from the graph?
2. What does a correlation coefficient tell us about the strength of a relationship?
3. How can outliers affect the line of best fit?
4. What is the difference between positive and negative correlation?
5. How can residuals help determine the accuracy of the best-fit line?

**Tip:** When interpreting a scatter plot, always look at the direction (upward/downward), the spread of the data points, and how closely they follow the trendline to understand correlation.

The scatter plot shows the time spent watching TV and the time spent doing homework by each of 24 students last week. Also shown is the line of best fit for the data.

Fill in the blanks below.

(a) For these 24 students, as the time spent watching TV increases, the time spent doing homework tends to ▼(Choose one)

(b) For these 24 students, there is ▼(Choose one) correlation between time spent watching TV and time spent doing homework.

(c) Using the line of best fit, we would predict that a student watching 12 hours of TV would do homework for approximately ▼(Choose one)


Understand how to analyze scatter plots to determine the correlation between time spent watching TV and doing homework. This problem involves interpreting the line of best fit and predicting values based on the scatter plot. Suitable for students in Grades 7-9.

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