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

Question

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

4(a) . The statement is False. In a scatter plot, the response is usually shown on the vertical axis and the explanatory variable shown on the horizontal axis

4(b) The statement is True. r^2 is a statistical value which measures how close the data are to the fitted regression line. if all data points are on a single line with some slope value, it indicates that the model explains 100% variance of the data. In this case value of r^2 = 1.

4(c)The statement is True. Correlation is the statistical tool to measure the strength of linear relationship between two variable. The value of correlation coefficient ranges between -1 and +1. if the two variables are strongly related the coefficient of correlation will be close to 1.

4(d) The statement is True. Correlation measures the strength of linear relationship between two variables. Regression slope measures the steepness of the linear relationship betwwen the variables. It can take any value between - infinity and + infinity.Negative value of slope indicates negative correlation and vice versa. Hence the correlation coefficient and slope must always be of the same sign. But their value may be different.

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