Consider the regression model Yi = β0 + β1Xi + ui.a. Suppose you know that β0 = 0. Derive a formula for the least squaresestimator of β1.b. Suppose you know that β0 = 4. Derive a formula for the least squaresestimator of β1?
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Consider the regression model Yi = β0 + β1Xi + ui.
a. Suppose you know that β0 = 0. Derive a formula for the least squares
estimator of β1.
b. Suppose you know that β0 = 4. Derive a formula for the least squares
estimator of β1?
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- Define coefficients of the Linear Regression Model?Consider the regression model Yi = β0 + β1X1i + β2X2i + β3(X1i * X2i) +ui. a. ΔY>/ΔX1 = β1 + β3X2 (effect of change in X1, holding X2 constant).b. ΔY/ΔX2 = β2 + β3X1 (effect of change in X2, holding X1 constant).c. If X1 changes by ΔX1 and X2 changes by ΔX2, then ΔY =(β1+β3X2)ΔX1 + (β2 + β3X1)ΔX2 + β3ΔX1ΔX2.Suppose the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables. Y=α+βaA+βpP+εY=α+βaA+βpP+ε Now suppose that the estimate of the model produces following results: α=344.585α=344.585, ba=0.102ba=0.102, bp=−11.192bp=−11.192, sba=0.173sba=0.173, sbp=4.487sbp=4.487, R2=0.813R2=0.813, and F-statistic=11.361F-statistic=11.361. Note that the sample consists of 10 observations. 1.) According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures decrease or increase sales by approximately 102,813 or 11,192 gallons. Similarly, a $1 increase in the selling price decrease or increase sales by approximately 813,11,192 or 102 gallons. 2.)Which of the independent variables (if any) appears to be statistically significant (at the 0.05…
- A realtor was investigating the price of real estate based on the size of the house in square feet x1 and if the house was within walking distance of an "A" rated public school. The indicator variable is defined as x = 1 if the house is within walking distance of an "A" rated public school and x = 0 if the house is NOT within walking distance of an "A" rated public school. If there was interaction in the regression problem, an appropriately fit regression model would have…? a) A different slope and different y-intercept for those within walking distance and those not. b) A different y-intercept for those that were within walking distance and those that were not; the slope would not change. c) A different slope, but not a different y-intercept for those within walking distance and those not. d) Cannot be determinedBeing able to read regression results can help the manager use the information to make right decisions particularly in developing a marketing strategy. Assume that you are interested in finding whether the advertisement has a significant positive effect on sales. Which of the following is correct? A. lower standard errors of the estimates are better than higher standard errors B. as a rule of thumb, you are correct 95 % of the time in concluding that there is a positive and significant relationship between the advertising expenditures and sales if the coefficient attached to advertising expenditure is positive and the “t” value is at least 2 C. there is a positive significant relationship between advertising expenditure and sales if both the lower bound and the upper bound of the confidence interval are positive. D. the R2 shows the proportion of the variation in the sales as explained by the model which consists of the advertising expenditure plus some other determinants of sales…Consider a regression in which a coefficient suffers from downward omitted variable bias. If you add a regressor that controls for the omitted variable bias: Group of answer choices 1. Can’t determine 2. The new estimate will be smaller. 3. The new estimate will remain unchanged. 4. The new estimate will be larger
- 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.The table below shows the number, in thousands, of vehicles parked in the central business district of a certain city on a typical Friday as a function of the hour of the day. Hour of the day Vehicles parked(thousands) 9 A.M. 6.2 11 A.M. 7.4 1 P.M. 7.5 3 P.M. 6.6 5 P.M. 3.9 (a) Use regression to find a quadratic model for the data. (Let V be the number of vehicles and t be the time in hours since midnight. Round the regression parameters to three decimal places.) V = (b) Express using functional notation the number of vehicles parked on a typical Friday at 4 P.M., and then estimate that value. (Round your answer to two decimal places.) V = = thousandIf in a regression, there are many variables, two of them show a square relationship (for example, A and A^2), A and A^2 show a strong positive correlation. Is there any problem with the model specification
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