The following data is given: 3 4 14 12 9 _y 4 7 11 Use linear least-squares regression to determine the coefficients m and b in the function y mx + b that best fit the data. Use Eq. (6.5) to determine the overall error.
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- Which of the following does not need to be computed to determine a simple regression line? SSx SP "Y-hat" SSyThe following information pertains to a simple least squares regression for DEF Corporation: Mean value of the dependent variable 30Mean value of the independent variable 8Coefficient of the independent variable 3Number of observations 12 What is the "a" value for the leasts-quares regression model? a. 60b. 30c. 6d. 0The following estimated regression equation is based on 10 observations y = 30.12 + .60x1 + .48x2 SST = 680.3, SSR= 601.4, Sb1 = .0813 and Sb2 = .0567 a. Compute MSR and MSE b. Compute F and perform the appropriate F test. Use alpha = .05. c. Perform a t test for the significance of B1. Use alpha = .05. d. Perform a t test for the significance of B2. Use alpha = .05.
- Compute the least-squares regression equation for the given data set. Use a TI-84 calculator. Round the slope and y-Intercept to at least four decimal places.A forecaster used the regression equation Qt = a + bt + c1D1 + c2D2 + c3D3 and quarterly sales data for 2004I–2021IV (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1, D2 andD3 are dummy variables for quarters I, II, and III. DEPENDENT VARIABLE: QT R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 64 0.8768 107.982 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 30.0 12.80 2.34 0.0224 T 1.5 0.70 2.14 0.0362 D1 10.0 3.00 3.33 0.0015 D2 25.0 7.20 3.47 0.0010 D3 40.0 15.80 2.53 0.0140 Using the estimation results given above, the predicted level of sales in 2022II is _______ units.A forecaster used the regression equation Qt = a + bt + c1D1 + c2D2 + c3D3 and quarterly sales data for 2004I–2021IV (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 F-RATIO P-VALUE ON F OBSERVATIONS: 64 0.8768 107.982 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 30.0 12.80 2.34 0.0224 T 1.5 0.70 2.14 0.0362 D1 10.0 3.00 3.33 0.0015 D2 25.0 7.20 3.47 0.0010 D3 40.0 15.80 2.53 0.0140 What is the estimated intercept of the trend line in the second quarter?
- Compute the least-squares regression equation for the given data set. Round the slope and y-intercept to at least four decimal places. 2 4 7 6 6 5 3 3 4 2Given are five observations for two variables, x and y. xi 3 8 12 18 20 yi 54 57 50 24 11 -select your answer choices- b. The least squares line provided an (good, bad) fit; __ % of the variability in y has been explained by the estimated regression equation (to 1 decimal)Which of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero. a b1 X1 R2
- The following estimated regression equation is based on 10 observations yhat = 30.12 + .60x1 + .48x2 SST = 680.3, SSR= 601.4, Sb1 = .0813 and Sb2 = .0567 a. Compute MSR and MSE b. Compute F and perform the appropriate F test. Use alpha = .05. c. Perform a t test for the significance of B1. Use alpha = .05. d. Perform a t test for the significance of B2. Use alpha = .05.The following data shows the yearly income (in $1000) and age of a sample of seven individuals. Income (in $1000) Age 20 18 24 20 24 23 25 34 26 24 27 27 34 27 a. Develop the least squares regression equation. b. Estimate the yearly income of a 30-year old individual. c. Compute the coefficient of determination. d. Use a t test to determine whether the slope is significantly different from zero. Use level of significance as 0.05.The following partial JMP regression output for the Fresh detergent data relates to predicting demand for future sales periods in which the price difference will be .10. SE Fit = .165360573, s = .628152. Predicted Demand Lower 95% MeanDemand Upper 95% MeanDemand 31 8.181072245 7.842346262 8.519798229 StdErr IndivDemand Lower 95% IndivDemand Upper 95% MeanDemand 0.649552965 6.850522511 9.511621980 Click here for the Excel Data File (a) Report a point estimate of and a 95 percent confidence interval for the mean demand for Fresh in all sales periods when the price difference is .10. (Round your CI answers to 3 decimal places and other answer to 4 decimal places.) (b) Report a point prediction of and a 95 percent prediction interval for the actual demand for Fresh in an individual sales period when the price difference is .10. (Round your PI answers to 3 decimal places and other answer to 4 decimal places.) (c) StdErr Indiv Demand on…