Linear Interpretation and Scatterplot

Consider the scatterplot of midterm and final exam scores for a class of 20 students. Which of the following statements is incorrect?

• Both the correlation and slope are negative.

• The same number of students scored 100 on the midterm as did on the final.

• The same percentage of students scored below 50 on each exam.

• Most students who scored below 50 on the midterm also scored below 50 on the final.

• Some students scored higher on the final than they did on the midterm

Answer explanation

There is a moderate negative slope to the data, showing a moderate negative correlation. On each exam two students had scores of 100. On each exam nine students, or 45 percent, scored below 50 on the midterm, only three scored below 50 on the final. Six students scored above 50 on the final but below 50 on the midterm.

Tags

CCSS.HSF.LE.B.5

Consider the following three scatterplots in the image.

Which has the greatest correlation coefficient r?

• I

• II

• III

• They all have the same correlation coefficient.

• The question cannot be answered without additional information.

Answer explanation

The correlation coefficient is not changed by adding the same number to each value of one of the variables or by multiplying each value of one of the variables by the same positive number.

How many students took AP statistics in the year 2003?

• 47

• 48

• 52

• 53

• 58

Tags

CCSS.HSF.LE.B.5

Studies have shown a strong, positive, linear relationship between pH and hardness of water (measured in grains). What does linear mean in this context?

• The points in the scatterplot all line up.

• A straight line can be drawn through the points in the scatterplot.

• There is a positive correlation.

• Every increase in hardness yields the same constant increase in pH.

• As hardness increases by 1 grain, pH tends to change by a constant amount on average.

Answer explanation

The points in the scatterplot generally form a straight-line pattern. In other words, as the explanatory variable (hardness) changes, the response variable (pH) generally exhibits a constant rate of change. The other choices are all misconceptions of linearity.

Tags

CCSS.8.F.A.3

Which of the following gives a proper ordering?

Which scatter plot appears to be more linear?

• Scatter plot A,

• Scatter plot B

Which scatter plot shows a linear relationship between x and y?

• Graph A

• Graph B

• Graph C

• Graph D

Tags

CCSS.8.F.A.3

Pick the best description of the association

• Positive linear weak association with clusters

• Positive linear strong association

• Negative non linear weak association

• positive non linear association

Which scatter plot shows a negative relationship?

• Graph A

• Graph B

• Graph C

• Graph D

Tags

CCSS.HSA.REI.D.12

how would you describe this association?

• positive linear strong

• positive linear weak

• positive linear moderate

• no association

Tags

CCSS.HSF-LE.A.1B