Answer: c) About 16% of the variation in value of the car is explained by a linear relationship with the age of the car.
e) The correlation coefficient, r, is 0.397.
Step-by-step explanation:
Given that:
Coefficient of determination (r²) between two variables, age of car (x) and value of car (y) = 0.158
Correlation of determination (r²) of 0.158 = (0.158 × 100% = 15.8% of the variation between the two variables can be explained by the regression line). Hence, about 16% of the variation between age and value of car can be explained by the linear relationship.
Coefficient of correlation (r) = sqrt(r²) = sqrt(0.158) = 0.397
Correlation coefficient is the measure of the correlation that exists between two variables.
Option c and e are correct.
Given that the coefficient of determination is equals to 0.158.
[tex]r^{2}=0.158[/tex]
Convert into percentage.
[tex]r^{2}=0.158*100=15.8[/tex] %
It means that nearly 16 % variation between two variable.
It represent that About 16% of the variation in value of the car is explained by a linear relationship with the age of the car.
correlation coefficient, [tex]r=\sqrt{0.158}=0.397[/tex]
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