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.

(a) T F In a scatterplot, the response is shown on the horizontal axis with the explanatory variable on the vertical axis.

(b) T F If no data points deviate from a single line with nonzero slope, then the r 2 of the fitted regression model is 1. (Assume the values of the explanatory variable are not identical).

(c) T F If the correlation between the explanatory variable and the response variable is 0.9, then those two variables must be linearly related.

(d) T F In simple linear regression, the correlation coefficient and the sample slope always have the same sign (i.e. both are positive or both are negative).

(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

a. False as explanatory variable is on Horizontal axis and response variable is on Vertical axis

b. R2 is a statistic that will give some information about the goodness of fit of a model. In regression, the R2 coefficient of determination is a statistical measure of how well the regression line approximates the real data points. An R2 of 1 indicates that the regression line perfectly fits the data.

Answer is True

c. True as correlation between two variables indicate linear correlation

d. True slope and correlation coefficient have same sign.

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