When testing for heteroscedasticity in a linear regression model it is preferable to use the Breusch-Pagan test, as it is able to detect non-linear forms of heteroscedasticity and has fewer parameters to estimate in the auxiliary regression, compared to the White test.
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- If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4For the following exercises, consider this scenario: The profit of a company decreased steadily overa ten-year spam.The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands ofover the ten-year span, (number of units sold, profit) for specific recorded years: (46,600),(48,550),(50,505),(52,540),(54,495). Use linear regression to determine a function Pwhere the profit in thousands of dollars depends onthe number of units sold in hundreds.
- What is regression analysis? Describe the process of performing regression analysis on a graphing utility.What is extrapolation when using a linear model?The President of the Farmers Association wants to know how the amount of fertilizer and theamount of water given to plants affect their growth. The results were inputted into MINITABso as to fit the model.Regression Analysis: Growth versus Water, FertilizerThe regression equation isGrowth = ? + ? Water + ?FertilizerPredictor Coef SE Coef T PConstant 42.085 ** 3.118 0.009Water 0.178 0.386 0.460 0.654Fertilizer 5.790 0.952 6.083 *S = 6.159 R-Sq = 77.1%% R-Sq(adj) = 73.3%Analysis of VarianceSource DF SS MS F PRegression 2 1532.603 766.301 *** ****Residual Error 12 455.130 37.928Total 14 1987.733i. Write out the regression equation ii. What is the sample size used in this investigation? iii. Determine the values of *, ** and ***, ****
- The President of the Farmers Association wants to know how the amount of fertilizer and theamount of water given to plants affect their growth. The results were inputted into MINITABso as to fit the model.Regression Analysis: Growth versus Water, FertilizerThe regression equation isGrowth = ? + ? Water + ?FertilizerPredictor Coef SE Coef T PConstant 42.085 ** 3.118 0.009Water 0.178 0.386 0.460 0.654Fertilizer 5.790 0.952 6.083 *S = 6.159 R-Sq = 77.1%% R-Sq(adj) = 73.3%Analysis of VarianceSource DF SS MS F PRegression 2 1532.603 766.301 *** ****Residual Error 12 455.130 37.928Total 14 1987.733 iv. Conduct a hypothesis test, at the 5% level of significance, to determine whether ? issignificant. v. What would be the growth of the plant if 4g of fertilizer and 7g of ater was given to itdaily? vi. Carry out an F -test at the 1% significance level to determine whether the model issignificantThe accompanying scatterplot shows the relationship between the age of an internet user and the amount of time spent browsing the internet per week (in minutes). The accompanying residual plot is also shown along with the QQ plot of the residuals. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. A.The residual plot displays a fan shape; therefore the Normality condition is not satisfied.B.The QQ plot mostly follows a straight line; therefore the Normality condition is satisfied.C.The scatterplot shows a negative trend; therefore the Normality condition is satisfied.D.The residual plot shows no trend; therefore the Normality condition is not satisfied.The President of the Farmers Association wants to know how the amount of fertilizer and theamount of water given to plants affect their growth. The results were inputted into MINITABso as to fit the model.Regression Analysis: Growth versus Water, FertilizerThe regression equation isGrowth = ? + ? Water + ?FertilizerPredictor Coef SE Coef T PConstant 42.085 ** 3.118 0.009Water 0.178 0.386 0.460 0.654Fertilizer 5.790 0.952 6.083 *S = 6.159 R-Sq = 77.1%% R-Sq(adj) = 73.3%Analysis of VarianceSource DF SS MS F PRegression 2 1532.603 766.301 *** ****Residual Error 12 455.130 37.928Total 14 1987.733iv. Conduct a hypothesis test, at the 5% level of significance, to determine whether ? issignificant. [4]v. What would be the growth of the plant if 4g of fertilizer and 7g of ater was given to it
- The President of the Farmers Association wants to know how the amount of fertilizer and theamount of water given to plants affect their growth. The results were inputted into MINITABso as to fit the model.Regression Analysis: Growth versus Water, FertilizerThe regression equation isGrowth = ? + ? Water + ?FertilizerPredictor Coef SE Coef T PConstant 42.085 ** 3.118 0.009Water 0.178 0.386 0.460 0.654Fertilizer 5.790 0.952 6.083 *S = 6.159 R-Sq = 77.1%% R-Sq(adj) = 73.3%Analysis of VarianceSource DF SS MS F PRegression 2 1532.603 766.301 *** ****Residual Error 12 455.130 37.928Total 14 1987.733Explain why it is not a good idea to exclude an intercept, b0 , from any linear regression model?Which is an assumption of linear regression analysis? The mean of the residuals should be