Question

1. A linear regression has the following equation: y = -9x + 2. How much would y change by, if x increases by 4? Answer with a positive number if y increases, and a negative number if y decreases.

2.A linear regression has the following equation: y = -0.52x + 10, with a coefficient of determination R2 = 0.64. What is the correlation coefficient, rounded to two decimal places?

3. A linear regression has the following equation: y = -0.36x + 10, with a correlation coefficient of R = -0.49. What is the coefficient of determination, rounded to two decimal places?

4. A linear regression has the following equation: y = 5.38x - 4.37, with a coefficient of determination of R2 = 0.87. How would you describe this correlation?

Answer 1

1) Here we have

y = -9x + 2

So if x increases by 4 units then there will be an increase of (-9)*4 units.

So there will be an increase of -36 units in y.

i.e. y will decrease by 36 units.

2) Here we have

So the correlation coefficient is

3) Here we have

coefficient of correlation = r = -0.49

So  the coefficient of determination

4) Here the coefficient of determination = 0.52

This means that about 52% of the total variation in y is explained by this linear regression model.

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