The following experimental data points are to be fitted to this 3-model parameter equation: In(y) = a- b(x +c)-1 -16 -6 11 34 65 y 10 20 60 200 760 Using least square regression find the values of a, b, and c. Also find the value of coefficio of determination r.
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- Question 9 of 10, Step 1 of 2 The following table lists the birth weights (in pounds), x, and the lengths (in inches), y, for a set of newborn babies at a local hospital. Birth Weights and Lengths Birth Weight (in Pounds), x 8 7 6 9 10 8 3 3 7 11 Length (in Inches), y 20 18 16 21 19 20 15 16 16 21 Step 1 of 2 : Find an equation of the least-squares regression line. Round your answer to three decimal places, if necessary.Question 1 Provide an algebraic proof that the least squares estimator is not consistent when Cov(x,e)=0 with the regression model y =B1+B2E(x)+e where E(e)=0So that E(y) = B1 + B2E(x)Question 2: The estimated regression equation for a model involving two independent variables and 65 observations is: yhat = 55.17+1.1X1 -0.153X2 Other statistics produced for analysis include: SSR = 12370.8, SST = 35963.0, Sb1 = 0.33, Sb2 = 0.20.a. Interpret b1 and b2 in this estimated regression equation b. Predict y when X1 = 65 and X2 = 70. c. Compute R-square and Adjusted R-Square. d. Comment on the goodness of fit of the model. e. Compute MSR and MSE. f. Compute F and use it to test whether the overall model is significant using a p-value (α = 0.05). g. Perform a t test using the critical value approach for the significance of β1.Use a level of significance of 0.05. h. Perform a t test using the critical value approach for the significance of β2.Use a level of significance of 0.05.
- Problem 1: I have uploaded data (PCE-PDI.xls) for the US total personal consumption expenditures and total disposable income from 1971:1 to 2009:7. Divide the entire sample into two subsamples: 1971:01 to 1985:12 and 1986:01 to 2009:07. Here consumption expenditure (PCE) is the dependent variable and disposable income (PDI) is the independent variable. Let variable Y denotes consumption expenditure and variable X denotes disposable income. (a) Estimate a two-variable regression model for both subsamples and report the estimated results.Consider the following table containing unemployment rates for a 10-year period. Unemployment Rates Year Unemployment Rate (%) 1 4.1 2 5.4 3 10.3 4 4.2 5 6.5 6 4.9 7 5.1 8 8.1 9 10.4 10 9.8 Step 1 of 2 : Given the model Estimated Unemployment Rate=β0+β1(Year)+εi,Estimated Unemployment Rate=β0+β1(Year)+εi, write the estimated regression equation using the least squares estimates for β0β0 and β1β1. Round your answers to two decimal places.Although the Excel regression output, shown in Figure 12.21 for Demonstration Problem 12.1, is somewhat different from the Minitab output, the same essential regression features are present. The regression equation is found under Coefficients at the bottom of ANOVA. The slope or coefficient of x is 2.2315 and the y-intercept is 30.9125. The standard error of the estimate for the hospital problem is given as the fourth statistic under Regression Statistics at the top of the output, Standard Error = 15.6491. The r2 value is given as 0.886 on the second line. The t test for the slope is found under t Stat near the bottom of the ANOVA section on the “Number of Beds” (x variable) row, t = 8.83. Adjacent to the t Stat is the p-value, which is the probability of the t statistic occurring by chance if the null hypothesis is true. For this slope, the probability shown is 0.000005. The ANOVA table is in the middle of the output with the F value having the same probability as the t statistic,…
- QUESTION2 The data set provided by JOHN shows the number of yearly values of flood damage relief items represented by y and the annual rainfall (in centimetres) represented by x over a period of 10 years.y(000s) x (cm)4.0 1101.5 2501.2 2203.0 1503.0 4502.5 2002.0 2102.0 2301.1 2903.0 100 (a) Find the standard deviations of x and y. (b) Find the equation of the least-squares regression line, assuming that the value of the relief items for flood damage depend on the amount of rainfall. (c) Calculate the correlation coefficient using the…Let Yt be the sales during month t (in thousands of dollars) for a photography studio, and let Pt be the price charged for portraits during month t. The data are in the file Week 4 Assignment Chapter 12 Problem 64. Use regression to fit the following model to these data:Yt = a + b1Yt−1 + b2Pt + etThis equation indicates that last month’s sales and the current month’s price are explanatory variables. The last term, et, is an error term. If the price of a portrait during month 21 is $10, what would you predict for sales in month 21? Sales Price $400,000 $15 $1,042,000 $12 $1,129,000 $24 $1,110,000 $18 $1,336,000 $18 $1,363,000 $30 $1,177,000 $27 $603,000 $24 $582,000 $36 $697,000 $27 $586,000 $24 $673,000 $27 $546,000 $30 $334,000 $33 $27,000 $24 $76,000 $27 $298,000 $30 $746,000 $18 $962,000 $21 $907,000 $24Question 22: A least squares regression line : A- may be used to predict a value of y if the corresponding x value is given. B- implies a cause-effect relationship between c and y. C- can only be determined if a good linear relationship exists between x and y . D- All of these answers are correct.
- Question 19: Based on the data shown below, a statistician calculates a linear model y=−2.23x+48.46y=-2.23x+48.46. x y 4 40.7 5 36.2 6 34.1 7 34.3 8 28.9 9 28.3 10 27.8 11 25.5 12 19.4 13 19.9 Use the model to estimate the y-value when x=4x=4y = Use the model to estimate the y-value when x=8x=8y =Question 9 Assume a regression analysis yields a regression line with the value Y=$120,000 + $0.58X, where Y equals plant labor costs and X equals dollars of production output. If the company plans to produce $2,400,000 of product during the upcoming month, it would project plant labor costs to be: a. $324,000 b. $120,000 c. $204,000 d. $2,400,000We have been assigned to determine how the total weeklyproduction cost for Widgetco depends on the number ofwidgets produced during the week. The following modelhas been proposed:Y b0 b1X b2X2 b3X3 where X number of widgets produced during the weekand Y total production cost for the week. For 15 weeksof data, we found that SSR 215,475 and SST 229,228.For this model, we obtain the following estimated regressionequation (t-statistics for each coefficient are in parentheses):yˆ 29.7 19.8X 0.39X2 0.005X3(0.78) (0.62) (1.25)a For a 0.10, test H0: bi 0 against Ha: bi 0(i 1, 2, 3).b Determine R2 for this model. How can the high R2value be reconciled with the answer to part (a)?