Question

1. the table below shows the number of absences and test scores for a group of students.

number of absences 1 5 0 8 3 2 0 3
test score 98 67 93 52 88 86 90 83
a. create a scatter plot for the data and draw a line of fit.
b. using your line of fit, what do you predict the test score would be for
a student with 10 absences? is this an example of interpolation or
extrapolation?
c. is the data correlated? if yes, give the type and explain whether this
is a causal relationship. if no, explain why not.

Explanation:

Part a

Step1: Identify Coordinates

Each data point is (number of absences, test score). So the points are (1, 98), (5, 67), (0, 93), (8, 52), (3, 88), (2, 86), (0, 90), (3, 83).

Step2: Plot Points

On the scatter plot grid, plot each (x, y) where x is absences (x - axis) and y is test score (y - axis). For example, (0, 93) and (0, 90) are on x = 0, y ≈ 90 - 93; (1, 98) is x = 1, y = 98; etc.

Step3: Draw Line of Fit

Visually, the data shows a negative trend. Draw a line that approximates the trend, balancing the number of points above and below the line.

Part b

Step1: Analyze Line of Fit Trend

From the data, as absences (x) increase, test scores (y) decrease. Let's assume a linear line of fit. From the points, when x = 0, y is around 92 - 93; when x = 8, y = 52. The slope \( m=\frac{52 - 93}{8 - 0}=\frac{- 41}{8}\approx - 5.125\). So the equation is \( y=93-5.125x\) (approximate, using (0,93) as a point).

Step2: Predict for x = 10

Substitute x = 10 into the line of fit equation: \( y = 93-5.125\times10=93 - 51.25 = 41.75\approx42\) (the prediction may vary slightly based on the line of fit, but the key is the trend).

Step3: Interpolation vs Extrapolation

The original x - values (absences) range from 0 to 8. x = 10 is outside this range, so it's extrapolation.

Part c

Step1: Check Correlation

As the number of absences (x) increases, test scores (y) generally decrease. So there is a negative correlation.

Step2: Causal Relationship

More absences can cause a student to miss learning, which can lead to lower test scores. So this is a causal relationship because the number of absences (a factor that affects learning time) directly influences test scores.

Final Answers (Summarized)

a. Scatter plot with points plotted and a line of fit (as described).
b. Predicted test score (approximate, e.g., 42) and it is extrapolation.
c. Yes, negative correlation, and it is a causal relationship because absences can cause lower test scores due to missed learning.

Answer:

Step1: Check Correlation

As the number of absences (x) increases, test scores (y) generally decrease. So there is a negative correlation.

Step2: Causal Relationship

More absences can cause a student to miss learning, which can lead to lower test scores. So this is a causal relationship because the number of absences (a factor that affects learning time) directly influences test scores.

Final Answers (Summarized)

a. Scatter plot with points plotted and a line of fit (as described).
b. Predicted test score (approximate, e.g., 42) and it is extrapolation.
c. Yes, negative correlation, and it is a causal relationship because absences can cause lower test scores due to missed learning.