A researcher found a study relating the distance a driver can see, y, to the age of the driver, x. When researchers looked at the association of x and y, they found that the coefficient of determination was r = 0.542 Select two conclusions that the researcher can make from this data.
a.) About 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
b.) The correlation coefficient, r, is -0.736.
c.) About 74% of the variation in the driver's age is explained by a linear relationship with the distance that the driver can see.
d.) About 46% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
e.) The correlation coefficient, r, is -0.458.
f.) The correlation coefficient, r, is -0.271.

The coefficient of determination is denoted [tex]R^2 \ or \ r^2[/tex] which gives the percent of the variance in the dependent variable that is predictable from the independent variable.

Given, [tex]r^2= 0.542[/tex]

That means 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.

Also, [tex]r=\sqrt{0.542}\approx\pm0.736[/tex] , where r determines the correlation coefficient.

As driver;s age increases the distance he can see decreases, so there is a negative correlation between them.

So r= -736.

Hence, The correlation coefficient, r, is -0.736.

So, the correct options are a.) and b.)