Question

5. Suppose you have performed a simple linear regression model and ended up with = b0 + b1 x.

(a) In your own words, describe clearly what the coefficient of determination, , measures.  

(b) Suppose that your calculations produce = 0.91. What can you conclude from this value? Furthermore, what can you say about the strength and direction of the relationship between the predictor and the response variable?

Answer 1

Answer:

a)

The coefficient of determination, denoted R2 or r2 and pronounced "R squared", it measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It also one of the goodness of fit criteria, higher the R squared value better the model. Value lies between 0 to 1.

b)

Here R squared value is 0.91 which suggests that 91% of the dependent variable is predicted by the independent variable. As value is high, model is good for predicting dependent variable.

Strength and direction of the relationship can be explaned by using correlation coefficient. And we know that correlation coefficient is the square root of coefficient of determinnation.

i.e  

r = 0.9539.

From this value( close to 1)  we can say that strength of the relationship is very high. And value is positive , so direction of the relationship is positive.

i.e variables are highly and positively correlated.