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?
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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?
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- In the linear model ,E (X*u) = a)X*u b) 0 c) u d) none of tha aboveA company wants to use regression analysis to forecast the demand for the next quarter.In such a regression model, demand would be the independent variable. True or false?a. Trueb. FalseSuppose you have run four regression models: A, B, C, and D. You are going to make a decision on which one to use just based on the adjusted r² value. Here are the adjusted r² values for each model: A: 0.71 B: 0.57 C: 0.65 D: 0.76 Which regression model would you choose based on the adjusted r²? OD since it has the highest adjusted r² value B since it has the lowest adjusted r² OC since it has an adjusted r² between the adjusted r² of regressions B and D. Either B or C since they have the lowest adjusted r²
- 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)?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.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 determined
- Suppose you decide to estimate a student consumption function. After you run an OLS regression on your data set with 36 observations, you obtain the following. The estimated regression, along with standard errors and t-statistics, CO = - 47.143 + 0.9714 YD (se) (2.0307) (0.157) (t) ( ) (6.187) Where, CO : the average annual consumption expenditures of the students on items other than tuition and room. YD : the average annual disposable income (including gifts) of the students a) Interpret the slope and the intercept. b) Compute the test statistics ( t value and critical t ) for the intercept of the regression. Note that significance level is 0.10. c) Suppose that disposable income is increased by 1000 dollars on average. What would be the predicted consumption expenditures?Define coefficients of the Linear Regression Model?Given the regression equationY = 43 + 10Xa. What is the change in Y when X changes by +8?b. What is the change in Y when X changes by -6?c. What is the predicted value of Y when X = 11? d. What is the predicted value of Y when X = 29? e. Does this equation prove that a change in X causes a change in Y?
- 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:Suppose that an economist has been able to gather data on the relationship between demand and price for a particular product. After analyzing scatterplots and using economic theory, the economist decides to estimate an equation of the form Q= aPb, where Q is quantity demanded and P is price. An appropriate regression analysis is then performed, and the estimated parameters turn out to be a = 1000 and b = - 1.3. Now consider two scenarios: (1) the price increases from $10 to $12.50; (2) the price increases from $20 to $25. a. Do you predict the percentage decrease in demand to be the same in scenario 1 as in scenario 2? Why or why not? b. What is the predicted percentage decrease in demand in scenario 1? What about scenario 2? Be as exact as possible.Being 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…