Question

question 5
1 pts
an entomologist observes that crickets tend to chirp more frequently on warmer days. when a regression equation is constructed to predict temperature based on number of cricket chirps, the entomologist finds that the equation explains 67.6% of the variability in temperature. this means r is equal to approximately ______.
type your answer in the box below and round this answer to exactly two decimal places in order to earn credit.

Explanation:

Step1: Recall the relationship between \( r^2 \) and \( r \)

The coefficient of determination \( r^2 \) represents the proportion of the variance in the dependent variable that is predictable from the independent variable. The correlation coefficient \( r \) is the square root of \( r^2 \), and since the number of cricket chirps and temperature are likely positively related (more chirps on warmer days), \( r \) should be positive. Given \( r^2 = 0.676 \).

Step2: Calculate \( r \)

Take the square root of \( r^2 \): \( r=\sqrt{0.676} \). Calculating this, \( \sqrt{0.676} \approx 0.82 \) (since \( 0.82^2 = 0.6724 \), close to 0.676, and more precisely, \( \sqrt{0.676}\approx0.822 \), which rounds to 0.82 when rounded to two decimal places).

Answer:

0.82