MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Which of the following statements concerning the linear correlation coefficient are always true?
I: The value of the linear correlation coefficient always lies
between−1 and 1.
II: If the linear correlation coefficient for two variables is zero, then there is a strong linear relationship between the variables.
III: If the slope of the regression line is negative, then the linear correlation coefficient could be either negative or positive.
IV: A linear correlation coefficient of −0.82 suggests a stronger linear relationship than a linear correlation coefficient of 0.62.
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- if the slope is negative then is the correlation coefficient also negative?arrow_forwardWhich of the following statements concerning the linear correlation coefficient are true? I: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables. II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. III: The value of the linear correlation coefficient always lies between −1 and 1. IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of minus−0.82. A. II and III B. I and II C. III and IV D. I and IVarrow_forwardWhen two variables have a perfect linear relationship, the correlation coefficient is always 1. True Falsearrow_forward
- c) Show that the coefficient of determination, R², can also be obtained as the squared correlation between actual Y values and the Y values estimated from the regression model where Y is the dependent variable. Note that the coefficient of correlation between Y and X is Eyixi r = And also that ỹ = ŷ (18.75)arrow_forwardIt is known that the linear regression equation: y= -2.88+1.77x, with a coefficient of determination of 0.81. Based on the two information, the correlation coefficient isarrow_forwardConsider a two-dimensional scatterplot representing the relationship between two continuous variables. If the correlation coefficient is -1, then: a. All points lie in a straight line with a slope of -1. b. All points lie in a straight line with an unknown negative slope. c. All points do not lie in a straight line but the best fitting regression line has a slope of -1 d. There is a strong positive relationship between the two variables.arrow_forward
- Suppose that two variables, x and y, have a correlation coefficient of −0.77. Which of the following statements are true? You must make a selection for each option. Click once to place a check mark for correct answers and click twice to empty the box for the wrong answers. check all that apply There is a strong relationship between these two variables. As x increases, y decreases. The variables have a negative linear relationship. As x increases, y increases. There is a weak relationship between these two variables.arrow_forwardA linear regression analysis reveals a strong, negative linear relationship between x and y. Which of the following could possibly be the results from this analysis? (A) ŷ 13.1 27.4x, r = 0.85 (B) == 27.4+ 13.1x, r = -0.95 (D) == (C) ŷ 13.1+ 27.4x, r = 0.95 542 385x, r = -0.15 (E) 0.85 0.25x, r = -0.85arrow_forwardIn a simple regression analysis (where y is a dependent and x an independent variable), if the slope is positive, then it must be true that there is a positive correlation between x and y there is a negative correlation between x and y if x is increased, y must decrease None of the answers is correct.arrow_forward
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