Would adding this variable makes better prediction of weight? Explain why.Below, we'll discuss how to check the requirements using software and what to do when a requirement isn’t met. (8) Fit the regression model with X 1 added as an indicator variable. Obtain the family prediction intervals for the new bears Use a 90 percent confidence coefficient. Obtain the family interval estimates for the mean weight of new bears. Obtain prediction intervals for the new bears Use a 90 percent confidence coefficient. Obtain the interval estimates for the mean weight of new bears. For the given three new bears with the information bellow a. Compute the 95% family CIs for each of β 1 , β 2 , β 3 , β 4 , β 5 , β 6 use most efficient method. Are the any variables can be dropped from the model? Explain why. Explain the difference between the F test and the t test in part a and b. State H o and H a , t value, t critical value and p-value, decision rules and conclusion. State Ho and Ha, F value, F critical value and p-value, decision rules and conclusion. Conduct the F test for regression relation using α as. Is your conclusion consistent with your preliminary findings in part ( c ) ?ģ. State the alternatives, decision rule, and conclusion. Conduct the Brown-Forsythe test to determine whether the error variance varies with the level of predictor variables. Is your conclusion consistent with your preliminary findings in part (c)? h. Conduct the Breusch- Pagan test to determine whether the error variance varies with the level of predictor variables. Give the formula used to compute the expected normal score. Also obtain the coefficient of correlation between the ordered residuals and their expected values under normality to ascertain whether the normality assumption is tenable here. Prepare a normal probability plot of the residuals. Do the two plots provide the same information? State your conclusions. Plot the residuals e i against Y i , X 5 on separate graphs to ascertain whether any departures from regression model in 1.c are evident. Obtain the residuals e i and prepare a dot plot of the residuals. What information does the graph provide? b. Obtain a Matrix scatter plot for the Y variable and the 6 X variables. List all the assumptions for the model in part c.Ģ. For model given in part c list all the parameters and their estimates. Is it also true that ∑ i = 0 n ε i = 0 ? Why? Explain. According to least square regression properties, ∑ i = 0 n e i = 0 when regression model Y i = β 0 + β 2 X i 2 + β 3 X i 3 + β 4 X i 4 + β 5 X i 5 + β 6 X i 6 + β 7 X i 7 + ε i is fitted to a set of n cases by the method of least squares. Would a linear regression model used with the data establish a causation relation between the weight and the predict variables? Explain why? c. Were the data used in this study observational or experimental data? Explain why. Entertaining references are in Reader's Digest April, 1979, and Sports Afield September, 1981. This would be used because in the forest it is easier to measure the length of a bear, for example, than it is to weigh it. One goal of the study was to make a table (or perhaps a set of tables) for hunters, so they could estimate the weight of a bear based on other measurements. Wild bears were anesthetized, and their bodies were measured and weighed.
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