4. True or False? For each of the following statements, choose either true or fa

Question

4. True or False? For each of the following statements, choose either true or false.

(e) T F The use of simple linear regression to describe the association between price and sales implies equal differences in predicted sales when comparing periods with prices $10 and $11 and periods with prices $20 and $21.

(f) T F A correlation of 0.8 implies two variables are more strongly related than if the correlation between the two variables were -0.8. (g) T F The least squares regression line always passes through the point (¯x, y¯). (h) T F High correlation implies causation.

(i) T F If we reverse the role of x and y (that is, y becomes the explanatory variable and x becomes the response variable) we will get the same least squares regression line.

(j) T F If no data points deviate from a single line with nonzero slope, then the correlation coefficient of the fitted regression model is 1. (Assume the values of the explanatory variable are not identical).

(k) T F When an observation falls above the least squares regression line its residual is always positive.

Explanation / Answer

e. False as it describes the linear correlation.

f. False. Sign describes the direction otherwise both the values are equally strong.

g. True. This is fact that The least squares regression line always passes through the point (¯x, y¯)

h. False. Correlation does not imply causation.

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