Concept explainers
In Section 12.4, we presented a formula for
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Probability and Statistics for Engineering and the Sciences
- Consider the model Ci= B0+B1 Yi+ ui. Suppose you run this regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=0.0697828; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively. The total number of observations is 2950. The number of degrees of freedom for this regression is A. 2950 OB. 2948 OC. 2952 OD. 2arrow_forwardA trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x₁ = distance traveled (miles) and x₂ = the number of deliveries made. Suppose that the model equation is Y = -0.800+ 0.060x₁ +0.900x₂ + e (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? hr (b) How would you interpret ₁ = 0.060, the coefficient of the predictor x₁? O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a one-mile (i.e.…arrow_forwardIn a study, the simple linear regression equation was found as y = - 2.65 + 3.23 * x. Accordingly, if the value of x is 1.55, what will be the value of "y"? Biraraştımada basit doğrusal regresyon denklemi y-265+3,23xolarak bulunmuştur. Buna yöre xin değeri 1,55 olursa y'nin değeri ne olur?- 25 - O A) -2,36 O B) 2,36 O C) 6,32 O D) -7,66 O E) 7,66arrow_forward
- Calculate the equation of the regression line and calculate the correlation coefficientarrow_forwardThis table reports the regression coefficients when the returns of the size-institutionalownership portfolio (columns 1 and 2) returns are regressed on three variables: a constant(column 3), the stock market returns (column 4), and the change of the value weighted discountof the closed end fund industry (column 6). Columns 5 and 7 report the corresponding t-statistics of the coefficient estimates. Note that a t-statistic with an absolute value above 1.96means the coefficient estimate is significantly different from 0 at the 1% level. Column 8reports the R square of the regressions. Column 9 reports the mean institutional ownership ofeach portfolio. The last column reports the F-statistics for a multivariate test of the null hypothesis that the coefficient on ΔVWD in the Low (L) ownership portfolio is equal to theHigh (H) ownership portfolio. Two-tailed p-values are in parentheses. 1. What is the main finding of this Table? 2. What is the explanation for…arrow_forwardConsider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certainarrow_forward
- A trucking company considered a multiple regression model for relating the dependent variable of total daily travel time for one of its drivers (hours) to the predictors distance traveled (miles) and the number of deliveries of made. After taking a random sample, a multiple regression was performed and the output is given below. Interpret the slope of the deliveries variable. When deliveries increases by 0.805 units, time increases by 1 hour, holding all other variables constant. 2) We do not have enough information to say. 3) When deliveries increases by 1 unit, time decreases by 0.805 hours, holding all other variables constant. 4) When deliveries decreases by 1 unit, time increases by 0.805 hours, holding all other variables constant. 5) When deliveries increases by 1 unit, time increases by 0.805 hours, holding all other variables constant.arrow_forwardShow the best fitted line on scatter diagram and Find the predicted value for each y using the exposure time and the equation obtained in part b (b. Find the equation of regression line between radiation doses on exposure time .usingleast square method)arrow_forwardWe are interested in estimating the following model log(wage) = Bo + Bieduc + Bzexper + u where • wage=hourly wage, in US dollars; • educ=number of years of education; • exper=number of years of work experience. The variable ctuit is the change in college tuition facing students from age 17 to age 18 and is used as an IV for educ. We run the first stage regression for educ and get the following output: Source s df MS Number of obs 1,230 F (2, 1227) 550.19 Model 3220.84426 2 1610.42213 Prob > F 0.0000 Residual 3591.43541 1,227 2.92700523 0.4728 R-squared Adj R-squared 0.4719 Total 6812.27967 1,229 5.54294522 Root MSE 1.7108 educ Coef. Std. Err. t P>|t| [95% Conf. Interval] ctuit -.1859575 .0608175 -3.06 0.002 -.3052752 -.0666398 exper -.521161 .0157156 -33.16 0.000 -.5519933 -.4903286 _cons 18.63905 .1757961 106.03 0.000 18.29415 18.98394 Is the assumption of instrument relevance satisfied? Why yes, or why not?arrow_forward
- Suppose the regression in Equation is estimated using LoSTR andLoEL in place of HiSTR and HiEL, where LoSTR = 1 - HiSTR is anindicator for a low-class-size district and LoEL = 1 - HiEL is an indicatorfor a district with a low percentage of English learners. What are thevalues of the estimated regression coefficients?arrow_forwardA trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x, = distance traveled (miles) and x, = the number of deliveries made. Suppose that the model equation is Y = -0.800 + 0.060x, + 0.900x2 + € (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? 5.8 v hr (b) How would you interpret ß1 = 0.060, the coefficient of the predictor X1? o When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a…arrow_forwardThe monthly premium quoted by an insurance company for a critical illness policy was collected from a sample of 6 adult male smokers at different age. The data for the sample are shown: Age 28 25 50 39 47 31 Premium ($) 75 40 175 125 250 105 Using Age to predict premium, the Linear Regression equation is given by: ŷ =6.556X−112 and r2=0.813y^=6.556X−112 and r2=0.813 a. Identify the independent and Dependent variables. Dependent: Age Premium Independent: Age Premium b. Determine the slope. Slope = Slope = Round to 3 decimal places c. Determine |r||r| . |r|=|r|= Round to 3 decimal places d. Interpret rr : and e. Determine critical r value at 5% significance level and determine if there is a significant linear correlation exists. |r| critical=|r| critical= Round to 3 decimal places Linear Correlation:Linear Correlation: Significant Not Significant f. Predict the monthly premium for a 40 years old adult male smoker.…arrow_forward
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