Question

In a simple linear regression study between two variables x ( the independent variable) and y (the dependent variable), a random large sample is collected and the coefficient of correlation r = −.98 is calculated.

A)Which of the following conclusion may be made? Group of answer choices

x and y are almost perfectly correlated, and y increases as x is increased.

x and y are almost perfectly correlated, and y decreases as x is increased.

x and y are moderately correlated, and y increases as x is increased.

x and y are very poorly correlated since r close to -1.

B)Find the coefficient of determination, and interpret it.

Answer 1

A. since r = -0.98 that means value of r is very close to -1 so, x and y have strong negative correlation.

so, it can be said that x and y are almost perfectly correlated, and y decreases as x is increased.

B. coefficient of determination = r2 = (-0.98)2 = 0.9604

that is, the regression model explains 96.04% of the variability of the response data, so the regression model can be considered to be good.