For a regression model y = XB + u where u is N(0, o 1), y is nx1 matrix, X is nxp matrix, B is px1 matrix and u is nx1 matrix, a. derive the estimators B using the method of least squares
Q: Section 2: Short Essay Questions: 1. A source of constant discussion among applied econometricians…
A: Regressions are used to quantify the link between one variable and the other factors that are…
Q: You are given the estimated regression equation y=234-6.2X2+082X3 R-Square-0.42 (7.2) (0.95) (0.45)…
A: The formula to calculate the test statistic is given by, t=B2Standard Error of B2=-6.20.95=-6.526…
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Q: (f) Regression line drawn by the method of Least square is called as the line of (g) Link Relatives…
A: (f) Regression line drawn by the method of Least square is called as the line of best fit .…
Q: 1 Consider an estimated linear regression model with a response Y and four predictors X1, X2, X3,…
A: Response variable = Y = Annual sales (in $1000s) Predictor variables: = X1 (in $100s) = X2 (in…
Q: Consider the regression model Yi = β0 + β1X1i + β2X2i + β3(X1i * X2i) +ui. a. ΔY>/ΔX1 = β1 + β3X2…
A: Yi = b0 + b1X1i + b2X2i + ui, i = 1,……..,n Y - dependent variable X1, X2 - two independent…
Q: What is multicollinearity?Discuss causes and consequences of multicollinearity for OLS estimation.…
A: (a) In a multiple linear regression model which means a regression model with more than one…
Q: rue or False For a linear regression model including only an intercept, the OLS estimator of that…
A:
Q: A researcher estimated the following regression equation, Yt from the use of various amounts , X1…
A: Taking null hypothesis: B0=0 Alternative hypothesis: B1not=0 Then : t=B0-B0^/se(B0) where B0 is the…
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A: a. The regression model communicates can be characterized as the interest (amount sold) for pens as…
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A: As per the question, the least square regression model is given as: Purchase^=-33.8+0.019(income)…
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Q: Could someone answer this for me please You estimate a simple linear regression model using a sample…
A: Answer: As it is mentioned : Y= 97.25 +19.74*X(3.86) (3.42 interval estimate =99%
Q: Which of the following are plausible approaches to dealing with a model that exhibits…
A: Heteroscedasticity is used in regression where scedasticity refers to variance and hetero means…
Q: The assumption that the error terms in a regression model follow the normal distribution with zero…
A: OLS (Ordinary Least Squares): This method helps in estimating the unknown parameters in a linear…
Q: Section 2: Short Essay Questions: 1. A source of constant discussion among applied econometricians…
A: Regressions are used to quantify the link between one variable and the other factors that are…
Q: Problem 2 Consider the following regression model: log(y;) = 6o + Bilog(x1:) + B2x2i + B3x3i + u;…
A: The given regression model is expressed as follows:
Q: Let be the residual for observation i for an estimated regression model. If 1.2 and ez = -0.33 R2 is…
A: e1= 1.2 and e2=0.33 Here clearly R^2 is less than 1 and RSS definitely positive.
Q: You are given the estimated regression equation y=234-6.2X2+082X3 R-Square=0.42 (7.2) (0.95) (0.45)…
A: The formula for calculation will be, t =B2Standard Error of B2=-6.20.95=-6.526
Q: What assumption is violated when multicollinearity is present in the regression model?
A: Assumption 6 of Linear Regression Model i.e. multicollinearity Multicollinearity refers to the part…
Q: ABC, Inc., sells tea products to various customers. In recent years, profits have been declining.…
A: Regression analysis is a statistical tool for examining the connection between one or more…
Q: A multiple regression model has the estimated form y hat (estimated value of y)= 5 + 6x + 7w As w…
A: In multiple regression, dependent variable is regressed on two or more independent variables.
Q: In the multiple regression model, the assumption of no perfect collinearity is best described as:…
A: "Since you have asked multiple questions, we will solve first question for you .. If you want any…
Q: The regression equation to predict sales based on temperature is: Predicted sales = -2419.01+ 98.02…
A: Estimated regression equation is Predicted sales = -2419.01+ 98.02 (temperature)
Q: You are the manager of a firm that produces a vegetable cooking oil in Ghana. In order to make…
A:
Q: A website that rents movies online recorded the age and the number of movies rented during the past…
A: Sample size n = 25< 30 SE(b1) = 0.0827
Q: Question 3 Consider a multiple regression model predicting Calories = 6.53+ 30.84 BMIl + 90.14…
A: Calories=6.53+30.84BMI+90.14Gender+30.94AgeGender=0 if maleGender =1 if female Calories consumed by…
Q: A final step in regression analysis is an examination of the residuals in a residual plot. This…
A: There is an assumption of homoscedasticity which states that the residual should have same or equal…
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A: does not allow covariance between Uit and polpc allows covariance between ai and polpc
Q: 18 Calcurate the least square regression líne equation with the given X and Y values. Consider the…
A: X Y X2 XY 60 3.1 3600 186 61 3.6 3721 219.6 62 3.8 3844 235.6 63 4 3969 252 65 4.1 4225…
Q: When the R2 of a regression equation is very high, it indicates that all the coefficients are…
A: R2 indicates the co-efficient of determinations. The higher the values, the higher is the…
Q: Given the estimated multiple regression equation ŷ = 6 + 5x1 + 4x2 + 7x3 + 8x4 what is the predicted…
A: Multiple linear regression is used to explain the relationship between two or more independent…
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A: The least-squares method is one of the statistical analysis which determines the best fir for the…
Q: consider a regression model Yi=B1+B2Xi+ui and you estimated B2hat =0.3. This implies that a unit…
A: When B2hat = 0.3 Then a unit change in x is predicted to 0.3 unit change in Y.
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A: A linear regression model is used to explain the value of a variable on the basis of the value of…
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A: Given information: A regression model is given to predict the selling price of a house based on the…
Q: Consider the regression model Y; = B1X1¡ + B2X2; + B3 (X1i * X2;) + Uj. Show that (a) AY/AX1 = B1 +…
A: Given:Yi=β1X1i+β2X2i+β3(X1i* X2i) + Ui
Q: If the value of Durbin-Watson test statistic (d) for the classical linear regression model is close…
A: Option (c) is correct.
Q: When Y is regressed on X, B, > 0, sx# 0, sy# 0, and the fraction of the variation in Y explained by…
A: Note:- “Since you have asked multiple question, we will solve the first question for you. If you…
Q: The standard deviation of the error terms in an estimated regression equation is known as:
A: Error term is the left over variable in a model when independent and dependent variable are unable…
Q: you are given the following model, where u and v are error terms meeting all standard assumptions of…
A: The value of R square measures how the dependent variables are explained by independent variables.
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A: Regression analysis is an important technique of forecasting in the field of econometrics. It…
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A: Since you have asked multiple questions, we will answer the first three questions for you. If you…
Q: Question 15 When the R2 of a regression equation is very high, it indicates that all the…
A: The regression equation is written as follows: Y = b0+b1X Here, Y is the dependent variable b0 is…
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A: Estimated regression equation: Starting salary = 3200 + 550 x WAM
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Q: For the estimated regression equation ŷ= 15 + 6x1 + 5x2 + 4x1X2, a unit increase in x2, while…
A: Here, we calculate the given for the estimated regression equation by the following method given…
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A: R2 = 0.45 Adjusted R2 = 1 - [(n-1) *(1-R2) / (n-k-1)] Where n = total sample size k = number of…
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- As an auto insurance risk analyst, it is your job to research risk profiles for various types of drivers. One common area of concern for auto insurance companies is the risk involved when offering policies to younger, less experienced drivers. The U.S. Department of Transportation recently conducted a study in which it analyzed the relationship between 1) the number of fatal accidents per 1000 licenses, and 2) the percentage of licensed drivers under the age of 21 in a sample of 42 cities. Your first step in the analysis is to construct a scatterplot of the data. FIGURE. SCATTERPLOT FOR U.S. DEPARTMENT OF TRANSPORATION PROBLEM U.S. Department of Transportation The Relationship Between Fatal Accident Frequency and Driver Age 4.5 3.5 3 2.5 1.5 1 0.5 6. 10 12 14 16 18 Percentage of drivers under age 21 Upon visual inspection, you determine that the variables do have a linear relationship. After a linear pattern has been established visually, you now proceed with performing linear…1. Consider a linear regression model y = XB + € with E(e) = 0. The bias of the ridge estimator of 3 obtained by minimizing Q(B) = (y — Xß)¹ (y — Xß) + r(BTB), for some r > 0, is ——(X²X + r1)-¹8 1 (X¹X +rI)-¹3 r -r(XTX+rI) ¹8 r(X¹X+r1) ¹3The best way to interpret polynomial regressions is to: A. look at the t-statistics for the relevant coefficients. B. analyze the standard error of estimated effect. C. plot the estimated regression function and to calculate the estimated effect on Y associated with a change in X for one or more values of X. D. take a derivative of Y with respect to the relevant X.
- True or False For a linear regression model including only an intercept, the OLS estimator of that intercept is equal to the sample mean of the independent variable.Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed actress/actor ages in various years, find the best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 43 years. Is the result within 5 years of the actual Best Actor winner, whose age was 45 years? Best Actress 27 30 30 61 30 32 46 28 61 22 43 56 D Best Actor 42 39 38 45 51 49 59 51 38 57 45 34 Find the equation of the regression line. y = + (Round the constant to one decimal place as needed. Round the coefficient to three decimal places as needed.) The best predicted age of the Best Actor winner given that the age of the Best Actress winner that year is 43 years is years old. (Round to the nearest whole number as needed.) Is the result within 5 years of the actual Best Actor winner, whose age was 45 years? the predicted age is the actual winner's age.If we run a regression where y (bankruptcy) = f (factors potentially predicting bankruptcy), what is the dependent variable?
- Numerical Answer Only Type Question Enter the numerical value only for the correct answer in the blank box. If a decimal point appears, round it to two decimal places. Assume that the number of visits by a particular customer to a mall located in downtown Toronto is related to the distance from the customer's home. The following regression analysis shows the relationship between the number of times a customer visits(Y)per month and the distance(X, measured in km) from the customer's home to the mall. \[ Y=15-0.5 X \] A customer who lives30 kmaway from the mall will visi______ who lives10 km away. less times than a customerWater is being poured into a large, cone-shaped cistern. The volume of water, measured in cm³, is reported at different time intervals, measured in seconds. A regression analysis was completed and is displayed in the computer output. Regression Analysis: cuberoot (Volume) versus Time Predictor Coef SE Coef Constant -0.006 0.00017 -35.294 0.000 Time 0.640 0.000018 35512.6 0.000 s=0.030 R-Sq=1.000 R-sq (adj)=1.000 What is the equation of the least-squares regression line? Volume = 0.640 - 0.006(Time) Volume = 0.640 - 0.006(Time) Volume = -0.006 + 0.640(Time) Volume = - 0.006 + 0.640(Time?)A scatter plot shows data for the cost of a vintage car from a dealership (y in dollars) in the year a years since 1990. The least squares regression line is given by y-25,000 + 500z. Interpret the y intercept of the least squares regression line. Select the correct answer below O The predicted cost of a vintage car from a dealership in the year is 820.000 O The predicted cost of a vintage car from a dealershpin the year 1090 is 85,000. O The predicted cost of a vintage car from a dealershp in the year 1990 is sse. The yintercept should not be interpreted.
- 2. Consider a two variable regression model, which satisfies all the Gauss Markov assumptions except that the error variance is proportional to X² i.e.E(u?) = o²X? Y₁ = B₁ + B₂X₁ + Ui How would you obtain the best linear unbiased estimates from the above regression.Expedia wants to use regression analysis to build a model for airfare tickets prices in the states: Ticket prices = 30 + B1*Miles + E where Miles is measured in hundreds Coefficients 169.50 5.90 Intercept Miles (in hundreds) Which of the following is true? Standard Error 1.34 0.09 4 t Stat 126.85 61.28 P-value 0.000 0.002 If Miles increases by 1, then we predict ticket price to go up by $5.9. O If ticket price goes up by $1, then we predict Miles to go up by 590 miles. O If ticket price goes up by $100, then we predict Miles to go up by 590 miles. If Miles increases by 100, then we predict ticket price to go up by $5.9.A. B. Consider data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy (cigs). The following simple regression was estimated using data on n = 1,388 births: bwght = 119.772 (0.572) n = 1,388, 0.514 cigs (0.091) R² = 0.0227, where standard errors are shown in parenthesis. What percent of the variation in birth weight is explained by cigs? What is the predicted birth weight when cigs = 0? What about when cigs = 20 (one pack per day)? Comment on the difference.