Question

The following data sets can be modeled linearly. Data Set M: {(14,95),(9,85),(4,65),(6,80),(3,73),(12,107),(7,64),(12,86),(10,96),(9,64),(1,44)} Data Set N: {(13,109),(9,85),(4,65),(6,80),(3,63),(12,107),(7,76),(11,100),(10,96),(8,85),(1,44)} Use technology to find the correlation coefficient of each data set.

Part A: Which data set has a better linear model?
Part B: How do you know this?

B: ​Data set M has a correlation coefficient that is closer to 1.
B: ​Data set M has a higher correlation coefficient.
A: ​Data set M has a better linear model.
B: ​Data set N has a correlation coefficient that is closer to 1.
B: ​Data set N has a lower correlation coefficient.
A: ​Data set N has a better linear model.

Answer 1

The data set N has a better linear model.

Explanation:

The data for the two data sets is:

Data Set M: {(14,95), (9,85), (4,65), (6,80), (3,73), (12,107), (7,64), (12,86), (10,96), (9,64), (1,44)}

Data Set N: {(13,109), (9,85), (4,65), (6,80), (3,63), (12,107), (7,76), (11,100), (10,96), (8,85), (1,44)}

The Correlation coefficient can be computed in Excel using the function:

CORREL(array1, array2)

Consider the table attached below for the correlation for data M and N.

Correlation coefficient for data M = 0.81

Correlation coefficient for data N = 0.99

Closer the correlation value is to 1 or -1, the better is the linear model.

This is because the correlation value of 1 or -1 are considered as perfect correlation.

The correlation coefficient for data N is 0.99 which is approximately equal to 1.

Thus, the data set N has a better linear model.