Refer to the following computer output from estimating the parameters of the nonlinear model Y=aRbSCTd The computer output from the regression analysis is: DEPENDENT VARIABLE: LNY R-SQUARE OBSERVATIONS: 32 0.7766 VARIABLE INTERCEPT F-RATIO 32.44 P-VALUE ON F 0.0001 PARAMETER ESTIMATE STANDARD ERROR T-RATIO -2.17 3.43 -0.6931 4.66 -0.44 8.28 P-VALUE 0.0390 0.0019 0.0774 0.0826 0.32 LNR 1.36 LNS 0.24 -1.83 LNT 4.60 1.80 Based on the information in the table, the nonlinear relation can be transformed into the following linear regression model:
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- 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…Consider the output here from a regression in R. What is 3₂? Coefficients: Estimate (Intercept) 1.708 5.404 -1.478 9.531 X1 X2 X3 Std. Error 0.555 2.792 0.6 2.758Water 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?)
- You estimated a regression with the following output. Source | SS df MS Number of obs = 289 -------------+---------------------------------- F(1, 287) = 41986.64 Model | 664544048 1 664544048 Prob > F = 0.0000 Residual | 4542496.25 287 15827.5131 R-squared = 0.9932 -------------+---------------------------------- Adj R-squared = 0.9932 Total | 669086544 288 2323217.17 Root MSE = 125.81 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 43.81013 .2138056 204.91 0.000 43.38931 44.23096 _cons | 49.31707 16.96222 2.91 0.004 15.93094 82.70319…Q4. The Omantel firm has estimate the Sales of fibre internet connections in Oman with the related to advertising expenditure made by the company over the past 26 months. Following is the firm estimated results of the regression equation. DEPENDENT VARIABLE: Y R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 26 0.85121212 8.747 0.0187 PARAMETER STANDARD VARIABLE ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 7.6 6.33232 1.200 0.2643969 3.53 0.52228 ? 0.0001428 a. What is the dependent and independent variables in the above regression equation of Omantel firm? b. Calculate the estimated t-ratio. Test the slope estimates for statistical significance at the 10 percent significance level. d. Interpret the coefficient of determination.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.
- 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?5. The following estimated equation was obtained by OLS regression using quarterly data for 1978 to 1996 inclusive. Yt = 2.20+ 0.104Xt₁ - 3.48 Xt₂ + 0.34Xt3 (3.4) (0.005) (2.2) (0.15) Standard errors are in parentheses, the explained sum of squares was 109.6, and the residual sum of squares 18.48. a. Test at the 5% level for the statistical significance of the parameter estimates. b. Calculate the coefficient of determination.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:
- Thirty data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is DEPENDENT VARIABLE: R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 30 0.5300 13.79 0.0009 VARIABLE PARAMETER STANDARD T-RATIO P-VALUE ESTIMATE ERROR INTERCEPT 93.54 46.210 2.02 0.0526 -3.25 0.875 -3.71 0.0009 The percentage of the total variation in Y NOT explained by the regression is percent,1. Consider a linear regression model y = XB + € with E(e) = 0. The bias of the ridge estimator of 3 obtained by minimizing Q(B) = (y — Xß)¹ (y — Xß) + r(BTB), for some r > 0, is ——(X²X + r1)-¹8 1 (X¹X +rI)-¹3 r -r(XTX+rI) ¹8 r(X¹X+r1) ¹3a simple linear regression equation shows the relationship between-