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?
Select one answer for Part A and one answer for Part B.
B: Data set M has a higher correlation coefficient.
B: Data set N has a lower correlation coefficient.
B: Data set M has a correlation coefficient that is closer to 1.
A: Data set M has a better linear model.
B: Data set N has a correlation coefficient that is closer to 1.
A: Data set N has a better linear model.
Is it the first A and last B?
Yes, the correct answers are:
Part A: Data set N has a better linear model.
Part B: Data set N has a correlation coefficient that is closer to 1.
No, it is not the first A and last B. The correct answers for Part A and Part B are both B: Data set N has a lower correlation coefficient.
To find the correlation coefficient of each data set, you can use a statistical software or a spreadsheet program such as Excel. Here is how you can find the correlation coefficient using Excel:
1. Enter the data sets into separate columns in Excel. For example, enter Data Set M in columns A and B, and Data Set N in columns D and E.
2. Select an empty cell where you want the correlation coefficient to be displayed. For example, select cell G1 for Data Set M and cell G2 for Data Set N.
3. In the selected cell, enter the formula "=CORREL(B2:B12, A2:A12)" for Data Set M and "=CORREL(E2:E12, D2:D12)" for Data Set N. This formula calculates the correlation coefficient between the two columns of data.
4. Press Enter to calculate the correlation coefficient. The result will be displayed in the selected cell.
5. Compare the correlation coefficients for each data set. The data set with a higher correlation coefficient indicates a stronger linear relationship between the variables.
Based on the results, you can see that Data Set N has a lower correlation coefficient compared to Data Set M. This means that Data Set M has a better linear model since it has a higher correlation coefficient, indicating a stronger linear relationship between the variables.