Suppose that you fitted the model E(y) = β0 + β1x + β2x^2 to n = 20 data points and obtained the following MINITAB printout. Regression Analysis: y versus x, x-sq Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 2 41227.6 20613.8 981.61 0.000 Error 17 357.0 21.0 Total 19 41584.6 Model Summary S R-Sq R-Sq(adj) 4.58258 99.14% 99.04% Coefficients Term Coef SE Coef T-Value P-Value Constant 12.38 3.40 3.64 0.002 x 9.79 1.49 6.57 0.000 x-sq -2.319 0.138 -16.80 0.000 Regression Equation y = 12.38 + 9.79x - 2.319x-sq What is your estimate of the average value of y when x = 0? (Use the exact values found in the MINITAB output.)
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MINITAB was used to fit the model $y=\beta_{0}+\beta_{1} x_{1}+$ $\beta_{2} x_{2}+\varepsilon$ to $n=20$ data points, and the printout (top of page 628 ) was obtained. a. What are the sample estimates of $\beta_{0}, \beta_{1},$ and $\beta_{2}$ ? b. What is the least squares prediction equation? c. Find SSE, MSE, and $s$. Interpret the standard deviation in the context of the problem. d. Test $H_{0}: \beta_{1}=0$ against $H_{a}: \beta_{1} \neq 0 .$ Use $\alpha=.05$. e. Use a $95 \%$ confidence interval to estimate $\beta_{2}$. f. Find $R^{2}$ and $R_{t}^{2}$ and interpret these values. g. Use the two formulas given in this section to calculate the test statistic for the null hypothesis $H_{0}-\beta_{1}=\beta_{2}=0$.
A multiple linear regression model of the following form is fitted to a data set: Yi = ̠₀ + ̠₁xi₁ + ̠₂xi₂ + ̠i, ̠i ~ N(0, ̣²)i.i.d. The model is fitted using SAS and the following output is obtained: Source DF Sum of Squares mean Square F Value Pr > F Model 2 28.119 14.059 ? 0.0039 Error 3 0.715 ? Corrected Total 5 28.833 Variable Parameter Estimate Standard Error t Value Pr > |t| Intercept 2.105 0.422 4.99 0.0155 x₁ 1.242 0.119 10.42 0.0019 x₂ -0.195 0.439 ? ? (a) Find the sample size. (b) Find mean squared errors (MSE). (c) Find R². (d) Find the value for the F-test statistic. (e) What hypotheses the above F test for? Given α = 0.05, what conclusion will you have? (f) One wants to test H₀ : β₂ = 0 vs Hₐ : β₂ ≠ 0. Find the value of test statistic and make your conclusion at α = .05.
Sri K.
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