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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A: Model 1 dependent variable (Y) : GDP 4 independent variables(Xi) : EC, INF, OP, PIS Equation :…
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…
Q: An online clothing retailer examined their transactional database to see if total yearly Purchases…
A: As per the question, the least square regression model is given as: Purchase^=-33.8+0.019(income)…
Q: In a regression problem with 1 output variable and with a total number of 100 possible input…
A: Regression is a statistical technique used in finance, investing, and other fields to assess the…
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…
Q: A researcher wants to study the determinants of crime in Turkey. For this she has data 81 Turkish…
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…
Q: a- Write down the economic function for the above estimation by using the information obtained from…
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.
Q: A researcher wants to test the relationship between the number of years of formal education received…
A: A linear regression model is used to explain the value of a variable on the basis of the value of…
Q: A home appraisal company would like to develop a regression model that would predict the selling…
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.
Q: (Yi, X1i, X2i) satisfy the assumptions of the attachment. You are interestedin β1, the causal effect…
A: Regression analysis is an important technique of forecasting in the field of econometrics. It…
Q: XYZ company is interested in quantifying the impact of consumer promotions on the sales of its…
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…
Q: Using a sample of recent university graduates, you estimate a simple linear regression using initial…
A: Estimated regression equation: Starting salary = 3200 + 550 x WAM
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A: Simple linear regression is a regression model that gauges the connection between one free factor…
Q: Consider the following sample regressions for the linear, the quadratic, and the cubic models along…
A: The regression is a popular statistical tool used in fields like economics, investing and finance to…
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…
Q: A professor is interested in understanding the factors on which the grades a student obtains in her…
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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- Consider the simple regression model: y=0.56+1.56x+u Using this and assuming the estimated Var(y)=0.64 and the estimated Var(x)=3.07, what is the estimated Var(x+y)?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.Consider the simple linear regression model given by E(y) = 1.5 + 0.23*x where y is measured in litres and x is measured in dollars. What must be the value of the slope coefficient if x is measured in thousands of dollars while the unit of measurement of y is unchanged (i.e., x is divided by 1000)? Answer:
- Given the estimated multiple regression equation ŷ = 6 + 5x1 + 4x2 + 7x3 + 8x4 what is the predicted value of Y in each case? a. x1 = 10, x2 = 23, x3 = 9, and x4 = 12 b. x1 = 23, x2 = 18, x3 = 10, and x4 = 11 c. x1 = 10, x2 = 23, x3 = 9, and x4 = 12 d. x1 = -10, x2 = 13, x3 = -8, and x4 = -16The regression equation to predict sales based on temperature is: Predicted sales = -2419.01+ 98.02 (temperature). A correct interpretation of the slope would be that 1. as temperature goes up by 1 degree, sales are predicted to go down by 2419.01. 2. as temperature goes down by 1 degree, sales are predicted to go up by 2419.01. 3. as temperature goes up by 1 degree, sales are predicted to go down by 98.02. 4. as temperature goes up by 1 degree, sales are predicted to go up by 98.02. 5. None of the answer choices provides a correct interpretation of the slope.Consider a data set with 15 observations and consider a multiple linear regression model with 7 in-dependent variables. Assume you have estimated the model and you find that SST = 1,325 and SSR = 794.
- A simple regression analysis to estimate the demand for Chick-fil-A’s new premium super-sized spicy chicken sandwich is Q= 48-2p. If Chick-fil-A sets the price at $12 and Q=20, calculate the regression’s error term? Also, list five assumptions of the classical linear regression model.Past class data has shown that the regression line relating the final exam score and the midterm exam score for students who take statistics from the College of Information Technology and Engineering from Dr. Kalaw is: final exam = 50 + 0.5 × midterm One interpretation of the slope is a. students only receive half as much credit (.5) for a correct answer on the final exam compared to a correct answer on the midterm exam. b. a student who scored 0 on the midterm would be predicted to score 50 on the final exam. c. a student who scored 10 points higher than another student on the midterm would be predicted to score 5 points higher than the other student on the final exam. d. a student who scored 0 on the final exam would be predicted to score 50 on the midterm exam.Consider the following estimated regression model relating annual salary to years of education and work experience. Estimated Salary=11,722.40+3182.56(Education)+1202.44(Experience)Estimated Salary=11,722.40+3182.56(Education)+1202.44(Experience) Suppose an employee with 66 years of education has been with the company for 33 years (note that education years are the number of years after 8th8th grade). According to this model, what is his estimated annual salary?
- consider a regression model Yi=B1+B2Xi+ui and you estimated B2hat =0.3. This implies that a unit change x is prdicted to5 We are given a sample of n observations which satisfies the following regression model: yi = β0 + β1xi1 + β2xi2 + ui , for all i = 1, . . . , n. This model fulfills the Least-Squares assumptions plus homoskedasticity. (a) Explain how you would obtain the OLS estimator of the coefficients {β0, β1, β2} in this model. (You do not need to show a full proof. Writing down the relevant conditions and explain)Given the regression equation Y = 100 + 10X a. What is the change in Y when X changes by +3? b. What is the change in Y when X changes by -4? c. What is the predicted value of Y when X = 12? d. What is the predicted value of Y when X = 23? e. Does this equation prove that a change in X causes a change in Y?