Question 2 1. a. State the Simple Linear regression model and define the parameters. [5 marks] b. Find the regression equation for the data below with y as the dependent variable. X 12 66 38 70 22 27 28 47 14 68 Y 14 35 22 29 6 15 17 20 12 29 [15 marks] c. Complete the ANOVA table below using information from the table in (b) where necessary, Source of variation | Degrees of freedom | Sum of squares | Mean sum of squares | F-Ratio Regression | 1 | ......... | 594.447 | ......... Error | ......... | 26.453 | ......... Total | 9 | .........
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State the Simple Linear Regression model and define the parameters. The Simple Linear Regression model is given by: $$ y_i = \beta_0 + \beta_1 x_i + \epsilon_i $$ where: - $y_i$ is the dependent variable (response) for the $i$-th observation - $x_i$ is the Show more…
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The regression model for a certain problem is given as follows: ŷ = 39.2 - 0.04x where the following associate statistical parameters are being calculated as: Predictor SE Coef. T P Intercept (39.2) 2.005 19.52 0.0 Slope (-0.04) 0.00767 -5.24 0.0 S = 3.743, R² = 59.1%, R²(adj)= 57.0% Analysis of variance results are: Source DF SS MS F P Regression 1 385.2 385.2 27.49 0.0 Residual Error 19 266.2 14.01 Total 20 651.4 a) Test for significance of regression using α = 0.05. Find the P-value for this test. What conclusions can you reach? b) Estimate the standard errors of the slope and intercept. c) Find a 95% confidence interval on the slope and intercept. d) What proportion of total variability in y is accounted for by x?
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The following information is for a multiple regression model with two independent variables: Source Degree of Freedom Sum of Squares Regression 2 ? Error 18 120 Total 20 180 a. Determine the regression mean square (MSR) and the mean square error (MSE). (2 marks) b. Compute the overall F_STAT test statistic. c. Determine whether there is a significant relationship between Y and the two independent variable at the 0.05 level of significance. d. Compute the coefficient of multiple determination, r². e. Compute the adjusted r².
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