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3.3 Breakfast cereals. A regression model was fit to a sample of breakfast cereals. The response...
Breakfast cereal: ASSESS/USE. The regression model in Exercise 3.6 was fit to a sample of 36...
Breakfast cereal: ASSESS/USE. The regression model in Exercise 3.6 was fit to a sample of 36 breakfast cereals with calories per serving as the response variable. The two predictors were grams of sugar per serving and grams of fiber per serving. The partition of the sums of squares for this model is SSTotal=SSModel+SSE 17190=9350+7840 Calculate R2 for this model and interpret the value in the context of this setting. Calculate the regression standard error of this multiple regression model. Calculate...
A nutritionist wants to model the relation between calories, protein, fat, and carbohydrates in breakfast cereal....
A nutritionist wants to model the relation between calories, protein, fat, and carbohydrates in breakfast cereal. Using a random sample of 12 ready-to-eat breakfast cereals, she obtained the following data per 100g of cereal Protein(g) Fat(9) Carbohydrates(9) 89 83 88 81 81 Calories 373 380 389 370 355 381 357 387 347 385 386 377 87.1 3.8 4 3 93.7 10 3.2 32 - 3.4 3.2 9.1 5.5 6.4 1.8 7.9 1.8 3.6 3.9 6.4 3.6 6 1 73 89...
3. You have been asked to find if there is a correlation between the amount of...
3. You have been asked to find if there is a correlation between the amount of calories per serving in a bowl of cereal versus the amount of sugar (in grams) in the cereal. The following data has been given for examination. Calories Sugar 18 200 23 210 12 170 12 190 37 220 19 175 23 201 22 210 32 210 11 190 11 197 205 29 a. Create a scatterplot of the given data. Be sure you explain...
You have been told that the amount of education a person obtains will guarantee them a...
You have been told that the amount of education a person obtains will guarantee them a high paying job. That is, their pay depends on their education. Discuss problems with this statement. Give a specific example of an individual that would be considered an outlier of this data set. You have been asked to find if there is a correlation between the amount of calories per serving in a bowl of cereal versus the amount of sugar (in grams) in...
Empirical Exercises 10.26. Klein and Goldberger attempted to fit the following regression model t...
Empirical Exercises 10.26. Klein and Goldberger attempted to fit the following regression model to the U.S. economy: 343i where Y= consumption, X2 = wage income, X3-nonwage, nonfarm income, and X4farm income. But since X2, X3, and X4 are expected to be highly collinear, they obtained estimates of and A from cross-sectional analysis as follows: Year 1936 62.8 43.41 17.10 3.96 1937 65.0 46.44 18.65 5.48 1938 63.9 44.35 17.09 4.37 1939 67.5 47.82 19.28 4.5 1940 71.3 51.02 23.24 4.88...
When evaluating a multiple regression model, for example when we regress dependent variable Y on two...
When evaluating a multiple regression model, for example when we regress dependent variable Y on two independent variables X1 and X2, a commonly used goodness of fit measure is: A. Correlation between Y and X1 B. Correlation between Y and X2 C. Correlation between X1 and X2 D. Adjusted-R2 E. None of the above
Question 2: Suppose that we wish to fit a regression model for which the true regression...
Question 2: Suppose that we wish to fit a regression model for which the true regression line passes through the origin (0,0). The appropriate model is Y = Bx + €. Assume that we have n pairs of data (x1.yı) ... (Xn,yn). a) From first principle, derive the least square estimate of B. (write the loss function then take first derivative W.r.t coefficient etc) b) Assume that e is normally distributed what is the distribution of Y? Explain your answer...
econometrics
Q2. A researcher specified regression model , in order toestimate effect of fertilizers and insecticides on corn production. Data for 10 years issummarized below:Where Y= bushels of corn per acre, X1 = amount of fertilizer in pounds per acre andX2 = amount of insecticides in pounds per acrei. Fit OLS regression equation and interpret itii. Using fitted regression equation, predict bushels of corn per acre produced ifamount of fertilizers used per acre is 30 pounds and amount of insecticides usedper...
1. Using question 12 (delaying major purchases) as the response variable (Y) compute a regression model...
1. Using question 12 (delaying major purchases) as the response variable (Y) compute a regression model with the following questions 9, 25 (gender: males as 0 and females coded as 1) as your predictor variables. You will have to use the data set Economic Gun Legislation Survey Regression Exercise posted for Week 9 on the webpage. Please do the following in exactly this order: a. Excel Output b. Model: write down model like in form y- b, b,X, -b.X. +...
2. Consider a simple linear regression i ion model for a response variable Y, a single...
2. Consider a simple linear regression i ion model for a response variable Y, a single predictor variable ,i1.., n, and having Gaussian (i.e. normally distributed) errors: This model is often called "regression through the origin" since E(X) = 0 if xi = 0 (a) Write down the likelihood function for the parameters β and σ2 (b) Find the MLEs for β and σ2, explicitly showing that they are unique maximizers of the likelihood function Hint: The function g(x)log(x) +1-x...
A nutritionist wants to model the relation between calories, protein, fat, and carbohydrates in breakfast cereal. Using a random sample of 12 ready-to-eat breakfast cereals, she obtained the following data per 100g of cereal Protein(g) Fat(9) Carbohydrates(9) 89 83 88 81 81 Calories 373 380 389 370 355 381 357 387 347 385 386 377 87.1 3.8 4 3 93.7 10 3.2 32 - 3.4 3.2 9.1 5.5 6.4 1.8 7.9 1.8 3.6 3.9 6.4 3.6 6 1 73 89...
3. You have been asked to find if there is a correlation between the amount of calories per serving in a bowl of cereal versus the amount of sugar (in grams) in the cereal. The following data has been given for examination. Calories Sugar 18 200 23 210 12 170 12 190 37 220 19 175 23 201 22 210 32 210 11 190 11 197 205 29 a. Create a scatterplot of the given data. Be sure you explain...
Empirical Exercises 10.26. Klein and Goldberger attempted to fit the following regression model to the U.S. economy: 343i where Y= consumption, X2 = wage income, X3-nonwage, nonfarm income, and X4farm income. But since X2, X3, and X4 are expected to be highly collinear, they obtained estimates of and A from cross-sectional analysis as follows: Year 1936 62.8 43.41 17.10 3.96 1937 65.0 46.44 18.65 5.48 1938 63.9 44.35 17.09 4.37 1939 67.5 47.82 19.28 4.5 1940 71.3 51.02 23.24 4.88...
Question 2: Suppose that we wish to fit a regression model for which the true regression line passes through the origin (0,0). The appropriate model is Y = Bx + €. Assume that we have n pairs of data (x1.yı) ... (Xn,yn). a) From first principle, derive the least square estimate of B. (write the loss function then take first derivative W.r.t coefficient etc) b) Assume that e is normally distributed what is the distribution of Y? Explain your answer...
1. Using question 12 (delaying major purchases) as the response variable (Y) compute a regression model with the following questions 9, 25 (gender: males as 0 and females coded as 1) as your predictor variables. You will have to use the data set Economic Gun Legislation Survey Regression Exercise posted for Week 9 on the webpage. Please do the following in exactly this order: a. Excel Output b. Model: write down model like in form y- b, b,X, -b.X. +...
2. Consider a simple linear regression i ion model for a response variable Y, a single predictor variable ,i1.., n, and having Gaussian (i.e. normally distributed) errors: This model is often called "regression through the origin" since E(X) = 0 if xi = 0 (a) Write down the likelihood function for the parameters β and σ2 (b) Find the MLEs for β and σ2, explicitly showing that they are unique maximizers of the likelihood function Hint: The function g(x)log(x) +1-x...
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