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- Determine the best (according to sum-of-squares-measure) curve y = Axb, through the dataabove.Transformed equation ln(y) = ln(A) + b ln(x)orY = a + bX.A “Cobb–Douglas” production function relates production (Q) to factorsof production, capital (K), labor (L), and raw materials (M), and an errorterm u using the equation Q = λKβ1Lβ2Mβ3eu, where λ, β1, β2, and β3 areproduction parameters. Suppose that you have data on production and thefactors of production from a random sample of firms with the same Cobb–Douglas production function. How would you use regression analysis toestimate the production parameters?The number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are under study. Suppose that the joint pmf of X and Y is modeled as fxy (x,y)=c(x+y), x=1,2,3 and y=1,2,3.Determine the marginal pmf of X. Determine the conditional pmf of Y given X=2.
- 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 F-RATIO P-VALUE ON F OBSERVATIONS: 32 0.7766 32.44 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT -0.6931 0.32 -2.17 0.0390 LNR 4.66 1.36 3.43 0.0019 LNS -0.44 0.24 -1.83 0.0774 LNT 8.28 4.60 1.80 0.0826 Based on the information in the table, if R = 1, S = 2, and T = 3, what value do you expect Y will have?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 F-RATIO P-VALUE ON F OBSERVATIONS: 32 0.7766 32.44 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT -0.6931 0.32 -2.17 0.0390 LNR 4.66 1.36 3.43 0.0019 LNS -0.44 0.24 -1.83 0.0774 LNT 8.28 4.60 1.80 0.0826 Based on the information in the table, if S increases by 8% (all other things constant), Y will MultipleA student used multiple regression analysis to study how family spending (y) is influenced by income(x1), family size (x2), and additionsto savings(x3). The variables y, x1, and x3 are measured in thousandsof dollars. The following results were obtained.ANOVAdf SSRegression 3 45.9634Residual 11 2.6218TotalCoefficients Standard ErrorIntercept 0.0136x10.7992 0.074x20.2280 0.190x3-0.5796 0.920 Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.
- A student used multiple regression analysis to study how family spending (y) is influenced by income(x1), family size (x2), and additionsto savings(x3). The variables y, x1, and x3 are measured in thousandsof dollars. The following results were obtained.ANOVAdf SSRegression 3 45.9634Residual 11 2.6218TotalCoefficients Standard ErrorIntercept 0.0136x10.7992 0.074x20.2280 0.190x3-0.5796 0.920 Carry out a test to determine whether y is significantly related to the independent variables.Use a 5% level of significance.A student used multiple regression analysis to study how family spending (y) is influenced by income(x1), family size (x2), and additionsto savings(x3). The variables y, x1, and x3 are measured in thousandsof dollars. The following results were obtained. ANOVA df SSRegression 3 45.9634Residual 11 2.6218Total Coefficients Standard Error Intercept 0.0136x1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 -Write out the estimated regression equation for the relationship between the variables. (1mark)-Compute coefficient of determination. What can you say about the strength of thisrelationship? -Carry out a test to determine whether y is significantly related to the independent variables.Use a 5% level of significance.-Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.he following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The multiple coefficient of determination is
- Determine the best (according to sum-of-squares-measure) curve y = Axb, through the data above. Transformed equation ln(y) = ln(A) + b ln(x) or Y = a + bX.The prelim grades (x) and midterm grades (y) of a sample of 10 MMW students is modeled by the regression line y = 12.0623 + 0.7771x. Estimate the prelim grade if the midterm grade is 83.A student used multiple regression analysis to study how family spending (y) is influenced by income(x1), family size (x2), and addition to savings(x3). The variables y, x1, and x3 are measured in thousandsof dollars. The following results were obtained.ANOVAdf SSRegression 3 45.9634Residual 11 2.6218TotalCoefficients Standard ErrorIntercept 0.0136x10.7992 0.074x20.2280 0.190x3-0.5796 0.920a. Write out the estimated regression equation for the relationship between the variables. b. Compute the coefficient of determination. What can you say about the strength of thisrelationship? c. Carry out a test to determine whether y is significantly related to the independent variables.Use a 5% level of significance. d. Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.