In simple linear regression, if the value of the correlation coefficient (r) is close to 1 or -1, what can we infer?A) The independent variable has no effect on the dependent variable.B) There is a weak linear relationship between the independent and dependent variables.C) The relationship between the variables is likely non-linear.D) There is a strong linear relationship between the independent and dependent variables.
Question
In simple linear regression, if the value of the correlation coefficient (r) is close to 1 or -1, what can we infer?A) The independent variable has no effect on the dependent variable.B) There is a weak linear relationship between the independent and dependent variables.C) The relationship between the variables is likely non-linear.D) There is a strong linear relationship between the independent and dependent variables.
Solution
D) There is a strong linear relationship between the independent and dependent variables.
In simple linear regression, a correlation coefficient (r) close to 1 indicates a strong positive linear relationship, meaning as the independent variable increases, the dependent variable also increases. Conversely, a correlation coefficient close to -1 indicates a strong negative linear relationship, meaning as the independent variable increases, the dependent variable decreases. Therefore, option D is correct.
Similar Questions
If there is no relationship (linear or otherwise) between two quantitative variables as observed on a scatterplot, the value of the correlation coefficient, r, is likely to be which of the following? Closer to 1 Closer to −1 Closer to 0 Either closer to −1 or 1
What does a correlation coefficient of -1 indicate? No linear relationship between two variables. A perfect positive linear relationship between two variables. A perfect negative linear relationship between two variables. The variables are unrelated.
Which of the following statements about the correlation coefficient is FALSE? It measures the strength and direction of a linear relationship. A value of 0 indicates no linear relationship. It can only take positive values. A value of -1 indicates a perfect negative linear relationship.
Suppose that the correlation r between two quantitative variables was found to be r = 0. Which of the following is the best interpretation of this correlation value? There is a strong linear relationship between the two variables. There is no linear relationship between the two variables. There is a strong relationship between the two variables. There is no relationship between the two variables.
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