Consider the two regressions models: ŷ Bo + Â₁×1 + ß₂x2 + B3X3 + B₁X4 + B5X5, where n-66 and R²=0.7 and ŷ = ß0 + Â₁×1 + ß₂x2, where n=66 and R²=0.1 Calculate the F-statistic for the joint test Ho : B3 = B4 = B5 = 0. Round to two decimal places
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- Consider the model Ci= B0+B1 Yi+ ui. Suppose you run this regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=0.0697828; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively. The total number of observations is 2950. The number of degrees of freedom for this regression is A. 2950 OB. 2948 OC. 2952 OD. 2Suppose we perform a simple linear regression (SLR) of two variables F1 and F2 against the same out variable (say y). The r-squared value/score of both the SLRS are 0.9678 and 0.95123 respectively for F1 and F2. Then what can you say about the correlation? O a. y is more dependent on F2 than F1 O b. None of these O . The result does not say that y is more dependent on F1 OR F2 O d.y is more dependent on F1 than F2Find the simple regression line y=α+βx for the pairs of points belonging to the independent and dependent variables (xi,yi) , respectively. Also, interpret the result by calculating the Pearson correlation coefficient. Please dont use excel.
- Using the least-squares regression line, y=-25.5+1.5x, what is the residual for the data point at (28,19)?A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Using data collected for a sample ofn 91 houses in East Meadow, the appraiser fit the data with the following simple, linear regression model: y = 91.80 + 19.72, where x = number of rooms and y = appraised value of the house (in thousands of dollars). Additionally, the appraiser determined the coefficient of correlation to be r = .93 and the coefficient of determination to be r %3D = .86. Give a practical interpretation of the coefficient of correlation. B IUS Ix E三 三 三 E E E Insert Formula IIA 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.
- A multiple regression was performed to estimate the model: y = Bo + B1X1 + B2X2 + B3X3 + ɛ A T-test with a = 0.05 was used to test if X3 is significant in the model. The calculated test statistic was Tcal = 2.36. If n = 25, what is your conclusion for this test? Reject Ho. There is evidence that X3 is significant in the model. Do not reject Họ. There is not evidence that X3 is significant in the model. Reject Ho. There is not evidence that X3 is significant in the model. Do not reject Ho. There is evidence that X3 is significant in the model.You have estimated a multiple regression model with 6 explanatory variables and an intercept from a sample with 46 observations. What is the critical value of the test statistic (tc) if you want to perform a test for the significance of a single right-hand side (explanatory) variable at α = 0.05? a.) 2.023 b.) 2.708 c.) 2.423 d.) 2.704A set of n = 25 pairs of X and Y values has a correlation of r = -0.50 with SSX = 38 and SSY = 14. Find the standard error of estimate for the regression equation. What percentage of the variance in Y is accounted for by X?
- A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings(x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained. ANOVA df SS Regression 3 45.9634 Residual 11 2.6218 Coefficients Standard Error Intercept 0.0136 x 1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 Required: 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.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 thousands of dollars. The following results were obtained. ANOVA df SS Regression 3 45.9634 Residual 11 2.6218 Total Coefficients Standard Error Intercept 0.0136 x1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 a. Write out the estimated regression equation for the relationship between the variables. b. Compute coefficient of determination. What can you say about the strength of this relationship? c. Carry out a test to determine whether y is significantly related to the independent variables. Use…An agribusiness performed a regression of wheat yield (bushels per acre) using observations on 21 test plots with four predictors (rainfall, fertilizer, soil acidity, hours of sun). The standard error was 1.02 bushels.