Suppose we use a person\'s dad\'s height to predict how short or tall the person
ID: 3240533 • Letter: S
Question
Suppose we use a person's dad's height to predict how short or tall the person will be by building a regression model to investigate if a relationship exists between the two variables. Suppose the regression results are as follows: Least Squares Linear Regression of Height Interpret the R-squared value in this problem. We can explain 26.73% of the variation in the sampled heights using dad's height in the linear model. We expect most of the sampled heights to fall within .2673 inches of their least squares predicted values. For every 1-inch increase in dad's height, we estimate height to increase by .2673 inches. At alpha = .05, there is insufficient evidence to indicate a positive linear relationship between height and dad's height.Explanation / Answer
In our example, the R2 we get is 0.2673. Or roughly 27% of the variance found in the response variable (DadsHt) can be explained by the predictor variable (Height). Example: If you were able to choose any metric to predict distance required for a car to stop, would speed be one and would it be an important one that could help explain how distance would vary based on speed?
I guess it’s easy to see that the answer would almost certainly be a yes. That’s we got a relative R2. Nevertheless, it’s hard to define what level of R2 is appropriate to claim the model fits well.
And consequently, a small p-value for the intercept and the slope indicates that we can reject the null hypothesis which allows us to conclude that there is a relationship between Height and Dad'sHT.
Answer :A