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3. Consider the following data for two variables, x and y. 4 5 4 6 4 6 9 5 11 a. Does there appear to be a linear relationship between x and y? Explain. b. Develop the estimated regression equation relating x and y. c. Plot the standardized residuals versus g for the estimated regression equation developed in part (b). Do the model assumptions appear to be satisfied? Explain. d. Perform a logarithmic transformation on the dependent variable y. Develop an estimated regression equation using the transformed dependent variable. Do the model assumptions appear to be satisfied by using the transformed dependent variable? Does a reciprocal transformation work better in this case? Explain

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The scatter diagram shows some evidence of a possible linear relationship. True. This is because we see that as x increases, y also increases linearly Scatter Plot btwn x and y 2 3 5 6 789b) The estimated regression equation relating x and y are 2.3220+0.6366*r [c) The residual plot indicates that the constant variance assumption is satisfied. True This is beacuse the points in the plot are random with no fixed pattern or order and the values seems evenly distributed positive and negative values.. Hence the constant variance assumption holds good. Residuals vis Predicted Values e?y = 1.452 + 2.747 * The model assumption holds good beacuse the points in the plot are random with no fixed pattern or order and the plot have evenly distributed positive and negative values. e) The reciprocal transformation is will not work better in this case. It is seen that the model assumption does not hold good and the R2 value has also reduced in this case. The R code for the above answers are as below: X=C12, 3, 4, 5, 7, 7, 7, 8, 9 y -CI4, 5, 4, 6,4,6,9, 5, 11) ## Question (a) ## plotixy, main- Scatter Plot btwn x and y) ## Question lb) ## summary fit) ## Question (c) ## res fits residuals pred fitsfitted.values plotipred, res, main- Residuals v/s Predicted Values) ## Question ld) log.x- log(x) plotfitlSfittedvalues, fiti residuals, main-Residuals v/s Predicted Values plotfit2sfitted.values, fit2sresiduals, main- Residuals v/s Predicted Values)

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