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.

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.

Step-by-step explanation:

The coefficient of determination is denoted  which gives the percent of the variance in the dependent variable that is predictable from the independent variable.

Given,

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, , 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.)

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step-by-step explanation: