Question

(a) Using technology, determine the correlation coefficient for the data to the nearest hundredth. Explain the steps you used.

a) The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables.
b) The correlation coefficient represents the proportion of the variance in one variable that can be predicted from the other variable.
c) The correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no linear correlation.
d) The correlation coefficient can be calculated using statistical software or calculators.

Answer 1

The correlation coefficient, denoted as r, is found using technology like statistical software or calculators by entering data into lists, selecting the linear regression function, and interpreting the output, which includes the value of r to show the strength and direction of the relationship between two variables.

Step-by-step explanation:

The correlation coefficient is a statistical measure that calculates the strength and direction of the relationship between two variables, often denoted as r. To calculate r using technology, one can utilize statistical software, spreadsheets, or scientific calculators with statistical functions.

To determine the correlation coefficient using a calculator such as the TI-83/84:

1. Enter the paired data into two lists, often labeled L1 for the x-values and L2 for the y-values.
2. Access the statistical analysis functions, typically found under the 'STAT' button followed by the 'CALC' menu.
3. Select the linear regression test option, often labeled LinRegTTest or similar.
4. The output screen will display the correlation coefficient r at the bottom, to the nearest hundredth as requested, signifying the strength and direction of the linear relationship.

The sign of r (+/-) indicates the direction (positive/negative) of the relationship, while the magnitude (number closest to 1 or -1) indicates the strength of the relationship. A perfect positive relationship would have an r of 1, a perfect negative relationship an r of -1, and no correlation an r of 0.