1) Suppose we use simple linear regression to analyze the relationship between a
ID: 3361310 • Letter: 1
Question
1) Suppose we use simple linear regression to analyze the relationship between a response variable Y and an explanatory variable X. If we reject H0: = 0 in favor of HA: 0, what can we conclude?
a) A linear relationship between X and Y is the best model.
b) The observed linear relationship is provides a better fit than a horizontal line.
c) Both (a) and (b).
d) Neither (a) nor (b).
2) Again, suppose we use simple linear regression to analyze the relationship between a response variable Y and an explanatory variable X. For a fixed value of X, namely X = x0, indicate which confidence interval is wider.
a) The 95% confidence interval for the mean value of Y when X = x0.
b) The 95% confidence interval for the predicted value of Y when X = x0.
Please answer both, I will be sure to give you thump up!
Explanation / Answer
1) If there is a significant linear relationship between the independent variable X and the dependent variable Y, the slope will not equal zero.
c) Both (a) and (b).
2) The prediction interval is always wider than the corresponding confidence interval of the prediction because of the added uncertainty involved in predicting a single response versus the mean response.
b) The 95% confidence interval for the predicted value of Y when X = x0.
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