Consider the following econometric modelbirthweight = Bo+B₁smoking + uwhere birthweight is a baby's weight at birth in grams and smoking is a dummy variable indicating whether the mother wassmoking during pregnancy (smoking = 1) or not (smoking = 0).What does B1 show?a.an estimate of the causal effect of smoking on birth weightb. the causal effect of smoking on birth weightC. the birth weight of a baby with a smoking motherd.the causal effect of birth weight on smoking

Consider the following econometric model birthweight = β0 + β1 smoking + u where birthweight is…

Answered: Consider the following econometric…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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12) Use computer software to find the best multiple regression equation to explain the variation in the dependent variable, Y, in terms of the independent variables, X1, X2, X3. 9896 29.1 1 421 9680 42.3 2 653 10449 29.8 3 573 10811 26.0 4 CORRELATION COEFFICIENTS 546 10014 34.3 5 499 10293 22.7 6 %3D 60% 0.00 Y/ X2=0.280 Y/ X3 = 0.930 504 9413 24.2 7 %3D 611 9860 31.6 8 %3D 646 9782 25.6 9 789 12139 37.9 10 COEFFICIENTS OF DETERMINATION 773 12166 33.9 11 YI X1 = 0.259 Y/ X2 = 0.079 YI X3 = 0.864 Y/ X1, X3 = 0.880 YI X1, X2, X3 = 0.884 753 9976 37.4 12 %3D 852 10645 27.0 13 %3D 755 9738 31.5 14 %3D 815 9933 39.9 15 %3D 902 10132 25.3 16 986 11145 30.4 17 909 9775 32.7 18 945 9549 35.0 19 866 10077 33.8 20 1178 11550 29.4 21 1230 10600 37.1 22 1207 11280 42.9 23 968 12100 32.2 24 1118 12420 30.5 25 A) Î = 57.8+0.036X, +28.1X3 B) Ý = -21.1+0.36X, +2.62X, +27.6X3 %3D C) Ý = 201.7+0.40X, +22.3X3 D) Y = 308.6+ 29.9X3 %3D
7.55 The following variables were recorded for several counties in Minnesota in 1977: y = average rent paid per acre of land with alfalfa X₁ = - average rent paid per acre for all land x₂ = average number of dairy cows per square mile x3 = proportion of farmland in pasture The data for 34 counties are given in Table 7.5 (Weisberg 1985, p. 162). Can rent for alfalfa land be predicted from the other three variables? (a) Find 3 and ². (b) Find , and ß using Sex and sx as in (7.46) and (7.47). (c) Find R² and R2.
A study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected. Average Distance Number of Facilities (miles) 1.67 11 1.11 16 0.82 21 0.62 27 0.50 30 0.47 (a) Develop a scatter diagram for these data, treating average distance traveled as the dependent variable. 1.8 T 35 1.8 1.8 1.6- 1.6- 1.6 30 1.4 1.4 1.4 1.2 25 1.2 1.2 1. 1. 1. 20 0.8 0.8 0.8 0.6 15 0.6 0.6- 0.4 0.4 0.4 10 0.2 0.2 0.2 0. 5 0. 0. 10 15 20 25 30 35 0. 0.2 0.4 0.6 0.8 1. 1.2 1.4 1.6 1.8 5 10 15 20 25 30 35 10 15 20 25 30 35 Number Distance Number Number (b) Does a simple linear regression model appear to be appropriate? Explain. O Yes, the scatter diagram suggests that there is a linear relationship. O No, the scatter diagram suggests that there is a curvilinear relationship. O No, the scatter diagram suggests that there is no relationship. (c) Develop an estimated…
Assume that you have collected a sample of observations from over 100 households and their consumption and income patterns. Using these observations, you estimate the following regression C₁ = Bo + B₁Y₁+H₁, where C is consumption and Y is disposable income. The estimate of B₁ will tell you: AIncome O A. APredicted Consumption OB. APredicted Consumption AIncome OC. Predicted Consumption Income OD. The amount you need to consume to survive.
12) The following results are an autoregression for US Exports to Mexico where the dependent variable is the lagged value of US Exports. a) Fill in the table b)Based on these regression results, what is your forecast of US Exports to Mexico for March 2005? c) Which of the two forecasts do you think is more accurate? Explain.
I’m interested in seeing whether or not there is a relationship between the number of hours someone sleeps and traffic accidents. I gather data from the Department of Transportation and get the following data: X (hours of sleep) Y (Traffic accidents) 5 2 5 1 3 4 4 4 2 6 6 3 8 1 9 1 5 0 6 4 Using the above data, create a linear regression equation to predict traffic accidents from hours of sleep. What is the Pearson correlation coefficient? Is it strong or weak? Positive or negative? What is the linear regression equation? (in the form of Y’ = bX + a) How many traffic accidents might we predict with someone that gets 0 hours of sleep? How many traffic accidents might we predict with someone that gets 11 hours of sleep?
1. The Gross Horsepower of a car can influence the mileage of the car. A random sample of 32 different cars’ Gross Horsepower and mileage (Miles/gallon) is collected. From the data, suppose you got the following results: Pearson’s correlation coefficient: -0.90 The fitted regression line: Ŷ = 30. 10 − 0. 07 X a. Identify the Independent and dependent variable. Give a justification of your answer.b. Interpret the value Pearson’s correlation coefficient. c. From the fitted regression line interpret the slope parameter. d. Find the value of R and comment. e. From the fitted model find the values of Y for given values of X as 110. How do you interpret this value?
A company wishes to estimate a regression line for the relationship between sales and advertising. а. To arrive at its decision regarding the best model to use, the company has calculated the following three correlation coefficients. i. ii. The sales in any month depend on that month's advertising with r = 0.28 The sales in any month depend on 50% of the previous month's advertising and 50% of that month's advertising with r= 0.68 The sales in any month depend on the previous month's advertising with r = 0.92 iii. Interpret each of the above correlation coefficients and state which of the suggested models you would choose as the basis for predicting sales. Justify your answer.
5. The National Center for Health Statistics published data on heights and weights. We obtained the following data from 10 randomly selected males 8-12 years of age. * y Height 69 Weight 151 72 154 70 160 200 Weight go IGO Regression Equation: Correlation r = 67 153 140 (20 O 75 201 66 126 a. If the researcher uses "Height" to predict "Weight" then the response variable is weight b. Use your calculator to create a scatter plot. Copy the scatter plot below (draw it). Make sure to label the horizontal axis and vertical axis, and provide the minimum and maximum values (displayed on your graph on your calculator) on each axis.. 70 174 71 185 60 70 Height 80 c. Is the association between the two variables positive or negative, or no association? (circle one) 68 143 g. Identify the slope of the regression line: and mention both men's heights and weights.)" d. Use your calculator to find the regression line (or line of best fit) and the correlation r. (Make sure something has a hat on it.) 65…
A linear regression analysis of Birth Weight (grams) and Gestational Age (weeks) gave the following output. c) What is the interpretation of the Beta Coefficient? d) What is the interpretation of the constant?
8. For the following data: a. Find the regression equation for predicting Y from X. b. Calculate the Pearson correlation for these data. Use r and SS, to compute SS standard error of estimate for the equation. and the residual Y 3 3 6. 9. 8 4 3 7 10 9.
In a study investigating maternal risk factors for congenital syphilis, syphilis is treated as a binary outcome variable, where 1 represents the presence of disease in a newborn and 0 represents absence of disease. The estimated coefficients from a logistic regression model containing the predictors cocaine or crack use, marital status, number of prenatal visits to a doctor, alcohol use and level of education are included in the table below. The estimated intercept is not included in the table. a. As an expectant mother’s number of prenatal visits to the doctor increases, does the probability that her child will be born with congenital syphilis increase or decrease?b. Marital status is a binary variable, where 1 indicates that a woman is unmarried and 0 indicates that she is married. What are the estimated relative odds that a newborn will suffer from syphilis for unmarried versus married mothers after holding the other variables in the model constant?c. Cocaine or crack use is also a…

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