You have a regression equation as follows: GDPt = α + β1Mt + β2Pt + ut where: t = time period GDPt = growth of gross domestic product (%) Mt = growth of money supply (%) Pt = percentage change of consumer price index (CPI) (%) ut = stochastic disturbance term 1) Based on the regression equation, construct the estimated regression equation. 2) Describe the residual precisely. Elucidate in what way it is related to ut.
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You have a regression equation as follows:
GDPt = α + β1Mt + β2Pt + ut
where:
t = time period
GDPt = growth of
Mt = growth of money supply (%)
Pt = percentage change of
ut = stochastic disturbance term
1) Based on the regression equation, construct the estimated regression equation.
2) Describe the residual precisely. Elucidate in what way it is related to ut.
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- 4. The following regression is fitted using variables identified that could be related to tuition charges ($) of a university. TUITION = a+ B ACCEPT + y MSAT + 1 VSAT Where ACCEPT = the percentage of applicants that was accepted by the university, MSAT = Median Math SAT score for the freshman class and VSAT = Median English SAT score for the freshman class. The data was processed using MNITAB and the following is an extract of the output obtained: Predictor Coef StDev Constant -26780 6115 ACCEPT 116.00 37.17 MSAT -4.21 14.12 VSAT 70.85 15.77 т P -4.38 0.000 0.003 -0.30 4.49 0.767 ** S = 2685 R-Sq 69.6% R-Sq (adj) = 67.7% Analysis of Variance Source DF SS MS Regression 3 Residual Error 49 Total 52 808139371 353193051 1161332421 269379790 7208021 F 37.37 Р 0.000 a) Write out the regression equation. b) State the dependent and independent variable(s) c) Fill in the blanks identified by ** and ****. d) Is significant, at the 10% level of significance? [1] [2] [6] [4] e) State one…Questions 1-30 refer to the following scenario: A company reports bi-annual (twice a year) sales data. The sales data for the last three years is shown in below Table. The intercept (a) of the regressions line (DV: Sales, IV: Obs) is equal to A 2 B 4 C 3 D 1 The slope (b) of the regressions line (DV: Sales, IV: Obs) is equal to a 4 b 2 c 3 d 1 The standard error of the regression is a 5.34 b 3.54 c 4.35 d 2.51 The standard error of the intercept is a 1.30 b 2.30 c 0.30 d 3.30 You want to test the hypothesis that the intercept is statistically significantly different from zero. To do so, you use the attached t-table. Your alpha (the risk you accept to make a Type I error) is a=0.1. How many degrees of freedom do you have? a n b n-2 c 4 d both b. and c. are correct You want to test the hypothesis that the intercept…An economic research centre has published data on GDP and Demand for refrigerators as given below:Year 2011 2012 2013 2014 2015 2016 2017GDP (billion) 20 22 25 27 30 33 35Refrigerator 50 60 80 80 90 100 120(a) Estimate regression equation R= a+by, where R= No of refrigerator sold and Y= GDP.Forecast demand for refrigerator in the year 2018 and 2019. The research centre has projected GDP for 2018 and 2019 at Rs. 38 billion and Rs. 40 billion respectively.
- The following estimated regression equation relating sales to inventory investment and advertising expenditures was given. ŷ = 21 + 13x1 + 9x2 The data used to develop the model came from a survey of 10 stores; for those data, SST = 19,000 and SSR = 14,630. (a)For the estimated regression equation given, compute R2. R2 = ?? (b)Compute Ra2. (Round your answer to two decimal places.) Ra2 = ?? (c)Does the model appear to explain a large amount of variability in the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to the nearest integer.) The adjusted coefficient of determination shows that (??) % of the variability has been explained by the two independent variables; thus, we conclude that the model does explain a large amount of variability.The 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.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?
- XYZ company is interested in quantifying the impact of consumer promotions on the sales of its packaged food product. XYZ has historical data on the following variables for 38 weeks: • Sales: Weekly sales volume in thousands of units.• Prom: Weekly spending on consumer promotions in thousands of Dollars" "A regression analysis was applied to XYZ historical dataset. The dependent variable is weekly Sales and the independent variables are weekly Prom and weekly Lagged Prom (i.e., last week Prom). This is a summary of the regression output:Sales = 0.80 + 1.20*Prom - 0.40*Lag(Prom) • R-squared=0.85• F-Statistic=23.83• p-value=0.001 (for the overall regression)•All regression coefficients are statistically significant at the 5% level." A. What will be the predicted sales volume ? B. What is the gross margin of this net volume impact due to $1000 spending per week on consumer promotions, if brand makes $2.20 gross margin per unit . C. What is the ROI of this promotion? D. What is predicted…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 Suppose that disposable income is increased by 1000 dollars on average. What would be the predicted consumption expenditures?1. Suppose output (Q) is related to labor (L) and capital (K) in the following nonlinear way: Q = albKc When taking log to this equation, it is transformed into a linear LnQ = Ina + b In(L) + c Ln (K) One hundred twenty-three observations are used to obtain the following regression results: Dependant Variable: Observations: Variable Intercept L K Q 123 5.5215 Parameter Standard Estimate error 0.650 R-square 0.350 0.7547 0.9750 0.2950 0.1450 F-ratio 184.56 t-ratio 5.66 2.20 2.41 p-value on F 0.00001 p-value 0.0001 0.0295 0.0173 a. Write the regression equation based on the output either in the transformed linear form or the original non-linear form.
- 1. 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 squaresWe estimate a simple regression explaining monthly salary (salary) in terms of IQ score (IQ), using data from a random sample of 935 individuals. We obtain the following estimated regression line: salary = 117 + 8.30 × IQ What is the correct interpretation of the estimated slope coefficient? Individuals with IQ scores of 100 have, on average, monthly wages of $830. An additional one point increase in IQ score is associated, on average, with an increase in monthly salary of $8.30. An additional one point increase in IQ score is associated, on average, with a decrease in monthly salary of $8.30. Each additional one point increase in IQ score will cause an increase in an individual's monthly salary by $8.30.Stores commonly offer a cheaper unit price for large quantity purchases. Quantity 1 2 5 10 20 Unit Price $100.00 $80.00 $70.00 $50.00 $40.00 a. Use regression to find a logarithmic equation to model the data. Round the numbers in your equation to 2 decimal places. y = a + bln(z) with You b b. Use your equation to find an appropriate unit price for a customer who purchases 15 items. c. Use your equation to find an appropriate unit price for a customer who purchases 25 items. $