8. Sixty pairs of measurements were taken at random to estimate the relation between variables X and Y. A least squares regression line was fitted to the collected data. The resulting residual plot is as follows: Which of the following conclusions is appropriate? A. A line is an appropriate model to describe the relation between X and Y. B. A line is not an appropriate model to describe the relation between X and Y. C. The assumption of normality of errors has been violated. D. The assumption of constant sample standard deviations has been violated. E. The variables X and Y are not related at all.
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Twenty pairs of measurements were taken at random to estimate the relation between variables X and Y. A least-squares line was fitted to the collected data. The resulting residual plot is shown. Which of the following conclusions is appropriate? A line is an appropriate model to describe the relation between X and Y. A line is not an appropriate model to describe the relation between X and Y. The assumption of the Law of Averages has been violated. The variables X and Y are not related at all. There is not enough information about the variables X and Y to form a conclusion.
Sri K.
Given are data for two variables, $x$ and $y$ \[ \begin{array}{c|ccccc} \boldsymbol{x}_{\boldsymbol{i}} & 6 & 11 & 15 & 18 & 20 \\ \hline \boldsymbol{y}_{\boldsymbol{i}} & 6 & 8 & 12 & 20 & 30 \end{array} \] a. Develop an estimated regression equation for these data. b. Compute the residuals. c. Develop a plot of the residuals against the independent variable $x .$ Do the assumptions about the error terms seem to be satisfied? d. Compute the standardized residuals. e. Develop a plot of the standardized residuals against $\hat{y}$. What conclusions can you draw from this plot?
Which of the following is not an assumption for the simple linear regression model? a. The error terms are independent of each other. b. The error terms have equal variances for all values of the independent variable. c. None of these. d. The distribution of the error terms will be skewed to left or right depending on the values of the dependent variable. e. The mean of the dependent variable for all levels of the independent variable can be connected by a straight line.
Ajiboye T.
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