Guided Example #2 - Regression and Correlation
Suppose randomly selected students are given the standard IQ test and the math component of the SAT to determine if a relationship exists between these two scores.
A partial list of the results appear in the table below:
|
IQ (x) |
103 |
113 |
119 |
107 |
128 |
153 |
111 |
128 |
135 |
|
SAT (Y) |
405 |
450 |
570 |
480 |
620 |
720 |
460 |
618 |
700 |
The researchers' hypothesize that students with higher IQ's have higher math SAT scores, and that IQ scores can predict the scores on the Math component of the SAT. A regression line for the data set above is y = 3.8 x+ 12.8. Which of the following is the most reasonable value for the correlation coefficient of the data set?
A. -2.7 B. -0.7 C. 4.8 D. 0.7
Step 1
The correlation coefficient r, is a number between -1, and 1, inclusive. Therefore, the only possible values for the correlation coefficient are -0.7, and 0.7. Since the slope of the regression line (3.8) for the data set is positive the most reasonable value for the correlation coefficient is 0.7.
All Steps
The correlation coefficient r, is a number between -1, and 1, inclusive. Therefore, the only possible values for the correlation coefficient are -0.7, and 0.7. Since the slope of the regression line (3.8) for the data set is positive the most reasonable value for the correlation coefficient is 0.7.