Question

ii) classify the above (1) to (6) as strong, moderate, weak or no correlation. iii) plot the following data as a scatter graph. a) classify the correlation as positive or negative or no correlation. b) if there is correlation, is it linear or non linear? is it strong, moderate or weak? hours slept | test score 8 | 83 7 | 86 7 | 74 8 | 88 6 | 76 5 | 63 7 | 90 4 | 60 9 | 89 7 | 81 (grid for plotting: test score on x - axis, # of hours slept on y - axis, with numbers 60, 65, 70, 75, 80, 85, 90 on x; 0 - 11 on y with a break.) also, scatter plots labeled with negative and no correlation and another.

Explanation:

Part III - Plotting the Scatter Graph

To plot the scatter graph, we use the given data where the x - axis represents the number of hours slept and the y - axis represents the test score. The data points are:

• (8, 83)
• (7, 86)
• (7, 74)
• (8, 88)
• (6, 76)
• (5, 63)
• (7, 90)
• (4, 60)
• (9, 89)
• (7, 81)

We mark each of these points on the coordinate plane with the x - value (hours slept) on the horizontal axis and the y - value (test score) on the vertical axis.

Part a - Classifying the Correlation (Positive, Negative, or No Correlation)

Step 1: Analyze the relationship

As the number of hours slept (x - variable) increases, we observe the general trend of the test score (y - variable). When we look at the data, as the number of hours slept increases from 4 to 9, the test score generally tends to increase (for example, 4 hours of sleep gives a score of 60, 5 hours gives 63, 7 hours gives scores like 86, 90, 81 and 9 hours gives 89). So, as one variable (hours slept) increases, the other variable (test score) also tends to increase.

Step 2: Determine the type of correlation

A positive correlation is when an increase in one variable is associated with an increase in the other variable. Since as hours slept increase, test scores generally increase, the correlation is positive.

Part b - Linear or Non - Linear Correlation and Strength

Step 1: Linear or Non - Linear

We check if the points seem to follow a straight - line pattern. When we plot the points (even mentally), the points seem to cluster around a straight - line trend. There is no obvious curve or non - linear pattern. So, the correlation is linear.

Step 2: Strength of Correlation

To determine the strength, we look at how closely the points cluster around the line of best fit. The points are not perfectly aligned (there is some spread), but they are relatively close to a straight line. This indicates a moderate positive linear correlation. If the points were very close to the line, it would be strong, and if they were very spread out, it would be weak. Since the points show a general upward trend and are somewhat clustered, it is a moderate positive linear correlation.

Answer:

s:

• III: Scatter plot with points (8, 83), (7, 86), (7, 74), (8, 88), (6, 76), (5, 63), (7, 90), (4, 60), (9, 89), (7, 81) marked.
• a): Positive correlation.
• b): Linear correlation, and it is a moderate correlation.