We have the following data for 17 countries: A researcher estimates a regression using the above data and obtains that: (a) Draw a scatter plot using M and G in each of the axes and explain why the researcher should expect that there is a problem of heteroscedasticity. (b) Explain the consequences of heteroscedasticity on the properties of the estimated coefficients.
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We have the following data for 17 countries:
A researcher estimates a regression using the above data and obtains
that:
(a) Draw a
the researcher should expect that there is a problem of
heteroscedasticity.
(b) Explain the consequences of heteroscedasticity on the properties of
the estimated coefficients.
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- Accountants at the GIll Co and Charted Brothers Accounting believed that several traveling executives were submitting unusually high travel vouchers upon returning from business trips. First, they took a sample of 200 vouchers submitted from the past year. Then they developed the following multiple-regression equation relating expected travel cost (Y) to a number of days on the road (X1) and distance traveled (X2) in miles: Y = 90.00 + 48.50X1 + 0.40X2 Here is additional information concerning the regression model: Sb1 = 0.038 Sb2 =0.019 R2 = 0.68 Se = 1.63 F-Statistic = 32.123 Durbin-Watson (d) statistic = 0.5436 What proportion of the total variation in expected travel cost is explained by the regression equation? Explain.In the method of regression, data sets are summarized in a useful form. The “independent” pieces of data are called inputs or regressors, whereas a quantity that is a function of the inputs, will be called a response. In an experiment, the effect of increasing storage temperature is related to the number of spoiled loaves of bread after 7 days. In this case, which variable will be the regressor?Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below. (a) What proportion of the variation in MCAS score is explained by the explanatory variables? (b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly. (c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly. (d) Suppose a second regression model (Model 2) was generated using only…
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- A researcher has developed a regression model from fourteen pairs of data points. He wants to test to determine if the slope is significantly different from zero. He uses a two-tailed test and a = 0.01. The critical tablet value is 2.718 3.012 2.650 O 3.055 O 2.168Fit these three regression models and then discuss the similarities and differences between them, particularly as relates to slope estimates (use CI’s) and R2. Also address why this is a “special case” and we wouldn’t necessarily expect to see these model characteristics for a typical dataset. a) Additive model including both predictors (output attached) b) Model including only Moisture (output attached) c) Model including only Sweetness BrandLiking = 68.62 + 4.38 Sweetness Term 95% CI P-ValueConstant (50.16, 87.09) 0.000Sweetness (-1.46, 10.21) 0.130 S R-sq R-sq(adj)10.8915 15.57% 9.54%The table below gives the number of weeks of gestation and the birth weight (in pounds) for a sample of five randomly selected babies. Using this data, consider the equation of the regression line, ŷ = bọ + b1x, for predicting the birth weight of a baby based on the number of weeks of gestation. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Weeks of Gestation 33 34 36 38 41 Weight (in pounds) 6. 6.1 6.8 7.3 7.9 Table Copy Data Step 5 of 6: Find the error prediction when x = 36. Round your answer to three decimal places.
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