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?Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?The Mayor of texas whom is partners with a local agriculturalist wants to know how the amount of fertilizer and the amount of water given to plants affect their growth. The results were inputted into MINITAB so as to fit the model a) Write out the regression equation b) What is the sample size used in this investigation? c) Determine the values of *, ** and ***, **** d) Conduct a hypothesis test, at the 5% level of significance, to determine whether ? is significant. e) What would be the growth of the plant if 4g of fertilizer and 7g of ater was given to it daily? f) Carry out an F -test at the 1% significance level to determine whether the model is significant
- More cereal Exercise 1 describes a regression model thatestimates a cereal’s potassium content from the amountof fiber it contains. In this context, what does it mean tosay that a cereal has a negative residual?Given a generic data set (x,y) with a linear regression. How do you determine if the y(dependent) will be less/greater than a certain value at a decided value of x?A business statistics professor would like to develop a regression model to predict the final exam scores for students based on their current GPAs, the number of hours they studied for the exam, the number of times they were absent during the semester, and their genders. The data for these variables are given in the accompanying table at the bottom of this page. a) Using Excel, construct a regression model using all of the independent variables. Create the dummy variable Gen, which equals 1 for a male and 0 for a female student ( this assignment is arbitrary) complete the regression equation for the model below, where y= Score, x1= GPA, x2= Hours, x3= Absenses, and x4= Gen. y= (__) + (__)x1 + (__)x2 + (__)x3 + (__)x4 b) Test the significance of the overall regression model using a= 0.10. c) interpret the meaning of the regression coefficient for the dummy variable. d) using the p-values, identify which independent variables are significant with a= 0.10. e) construct a regression…
- Given a generic data set (x,y) with a linear regression. How do you determine if the y(dependent) will be less than a certain value?Which is an assumption of linear regression analysis? The mean of the residuals should beAnd run a simple linear regression in SPSS to determine if pulse at warm-up (The name of the variable in SPSS is "stage 1" and its label is "pulse at warmup") significantly predicts pulse while running ( The name of the variable in SPSS is "stage 3" and its label is "pulse running"). Use α = .05 Is the regression equation significant? That is, does pulse at warm-up explains (or predicts) a significant amount of variability in pulse while running? Report the F, df (of numerator, and df of the denominator) and p-value.
- within the outpout attachted, define what analysis has been conducted and report the regression equation derived from the output and explain how an increase in the predictor variable would influence the outcome variableSuppose you would like to estimate Y= B1 + B2 X + B3 Z + u model using data from 40 firms. Suppose you are to perform Breuch-Pagan (LM type test) for homoscedasticity, define the auxiliary regression? Further suppose that you find R-squared from the auxiliary regression to be 0.85, carry out B-P test for homoscedasticity at %5 level of significance and interpret the result (Set the hypotheses).When should a regression model not be used to make a prediction?