A researcher estimated the following regression equation, Yt from the use of various amounts , X1 and X2 on a hectare basis using time series data from 2001 to 2010. The operation model is: Yt = B0 + B1X1 + B2x2 + ei The estimated regression equation is: Yt = 31.98 + 0.65X1 + 1.10X2 (0.24) (0.27) (0.25) Adjusted R2 = 0.989 Figures in parenthesis are standard error of estimates. i) Estimate the t-values for each of the coefficients

A researcher estimated the following regression equation, Yt from the use of various amounts , X1 and X2 on a hectare basis using time series data from 2001 to 2010. The operation model is: Yt = B0 + B1X1 + B2x2 + ei The estimated regression equation is: Yt = 31.98 + 0.65X1 + 1.10X2 (0.24) (0.27) (0.25) Adjusted R2 = 0.989 Figures in parenthesis are standard error of estimates. i) Estimate the t-values for each of the coefficients

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter4A: Problems In Applying The Linear Regression Model

Section: Chapter Questions

Problem 2E

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In the following regression Price = 119.2 +0.485BDR+23.4Bath + 0.156Hsize +0.002Lsize + 0.09 (23.9) (2.61) (8.94) (0.011) (0.00048) (0.311) (10.5) The F-statistic for omitting BDR and Age from the regression is F-statistic=0.08, which has a p-value=0.98. Are the coefficients on BDR and Age statistically significantly different from 0 at 5% level? Yes, significantly different from 0 since the p-value>0.05. O No, not significantly different from 0 since the p-value>0.05. We don't know O depends on sample size
(e) Suppose you have been given the following ordinary least squares (OLS) regression result. Estimated Long Run Coefficients using the ARDL Approach ARDL (1,2,2,2,0,2) selected based on Akaike Information Criterion Dependent variable is LY 33 observations used for estimation from 1987 to 2019 T-Ratio [Prob.] 4.6671[0.000] 4.6678[0.051] 7.9897[0.043] -4.802[0.009] 2.3898[0.028] 1.0498[0.308] Regressor Coefficient Standard Error 0.36068 0.45447 LK 0.077280 LM 0.097363 0.48751 -0.41208 0.19057 0.52521 LE 0.061017 LF 0.085800 LT 0.079744 C 0.500320 where, Y = Economic growth K = Capital M = Employment E = Electricity consumption F = Foreign direct investment T= Technology (i) Write the regression equation. Interpret the estimated coefficients. (ii) Which explanatory variables are significant at the 1%, 5% and 10% level? Which variables are insignificant? Briefly explain.
Suppose we estimated our multiple linear regression, all of the variables have p values below 0.05 (so they are statistically different from zero) but the intercept has p-value equal to p=0.343. What does it mean?
The linear regression equation, Y= a + bX, was estimated. The following computer output was obtained: DEPENDENT VARIABLE: Y OBSERVATIONS: 15 VARIABLE INTERCEPT Multiple Choice O X R-SQUARE 0.6010 PARAMETER ESTIMATE 412.18 0.6358 F-RATIO 19.58 STANDARD ERROR 102.54 0.1765 P-VALUE ON F 0.0001 T-RATIO P-VALUE 0.0015 0.0032 In the regression above, the parameter estimate of b (on the variable X) indicates that 4.02 3.60 X increases by 0.1765 units when Yincreases by one unit. X increases by 0.6358 units when Y increases by one unit. Y increases by 0.1765 units when X increases by one unit. Y increases by 0.6358 units when X increases by one unit. Y increases by 3.60 units when X increases by one unit.
Refer to the following computer output from estimating the parameters of the nonlinear model Y=aRbsc7d The computer output from the regression analysis is: DEPENDENT VARIABLE: LNY R-SQUARE 32 0.7766 OBSERVATIONS: VARIABLE INTERCEPT LNR P-VALUE ON F 0.0001 PARAMETER ESTIMATE STANDARD ERROR T-RATIO -0.6931 F-RATIO 4.66 -0.44 8.28 32.44 0.32 1.36 -2.17 3.43 -1.83 P-VALUE 1.80 0.0390 LNS 0.24 LNT 4.60 Based on the information in the table, the nonlinear relation can be transformed into the following linear regression model: Multiple Choice in Y= 1n a.ln R.1n S.1n T in Y= 1na + b1nR+ cins + din T 1n Y = 1n(aRb SC7d) Y = 1n(aRb Sc7d) 0.0019 0.0774 0.0826
7. Suppose we are interested in the relationship of the union status variable Y (= 1; if in union, = 0, if not in union) to the conditioning variables X₁ = gender (1 if female, 0 if male), and X2 = marital status (1 if married, 0 if not). Table below gives the coefficient estimates obtained in (i) Least squares regression of Y on X₁ and X₂, and, (ii) Nonlinear least-squares estimates of the logistic regression model E(YX1, X2) = G(Z), where Z=80+ B₁X1+B₂X2, and G(Z) = e²/(1+e2). In parenthesis are the conventional standard errors of the coefficient estimates. Also tabulated are the means of the conditioning variables (regressors).
Regression analysis was applied between $ sales (y) and $ advertising (r) across all the branches of a major international corporation. The following regression function was obtained. ŷ = 5000 + 7.25r (a) Predict the amount for sales where the advertising amount is $ 1,000,000.00. (b) If the advertising budgets of two branches of the corporation differ by $30,000, then what will be the predicted difference in their sales?
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…
The table below shows the average weekly wages (in dollars) for state government employees and federal government employees for 10 years Construct and interpret a 90% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $835. The equation of the regression line is hat (y) = 1366x + 35047. \table[[Wages (state), x, 700, 777, 781, 802, 838, 880, 908, 938, 949,983], [ Wages (federal), y, 1, 024, 1,048, 1, 096, 1, 150, 1, 182, 1, 235, 1, 265, 1, 304, 1, 334, 1, 404]] Construct and interpret a 90% prediction interval for the average weekly wages of federal government employees when the average weekly wages of state government employees is $835. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest cent as needed.) A. There is a 90% chance that the predicted average weekly wages of federal government employees is between $ and $ given a state…
Water 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 forecaster used the regression equation Qt= a + bt+q₁D₁ + C2D2 + c3D3 and quarterly sales data for 2004/-2021/V (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1, D₂ and D3 are dummy variables for quarters I, II, and III. DEPENDENT VARIABLE: QT R-SQUARE OBSERVATIONS: 64 0.8768 VARIABLE INTERCEPT T D1 D2 D3 F-RATIO P-VALUE ON F 107.982 0.0001 PARAMETER STANDARD ESTIMATE 30.0 1.5 10.0 25.0 40.0 ERROR T-RATIO P-VALUE 2.34 0.0224 2.14 0.0362 3.33 0.0015 3.47 0.0010 2.53 0.0140 12.80 0.70 3.00 7.20 15.80 In any given year, quarterly sales tend to vary as follows:
A linear regression model for the revenue data for a company is R=27.1t+203 where R is total annual revenue and t is time since 1/31/02 in years. 12 months 12 months 12 months Billions of Dollars Revenue Gross Profit 12 months 12 months ending 1/31/02ending 1/31/03ending 1/31/04 ending 1/31/05 ending 1/31/06 500- 201 49 236 54 255 60 500- 277 65 (A) Draw a scatter plot of the data and a graph of the model on the same axes. OA. B. O.C. KICB Q 2 316 72 500- oo D. 500- Q G