Using the following summary statistics to perform the linear regression. x? = 60.1, ? = 103.15, SSxx = 21.88, SSyy = 34.64, SSxy = -24.78, and n = 13.
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78}{60.1} \approx 0.412$ Intercept: $a = \bar{y} - b\bar{x} = 103.15 - 0.412(60.1) \approx 80.23$ Therefore, the linear regression equation is: $\hat{y} = 0.412x + 80.23$ Show more…
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Given the following quantities for a simple linear regression model results from a sample of size n=8 observations: Σx = 47.7, Σy = 324, Σx² = 304.59, Σy² = 14706, and Σxy = 1766.8 a) Use the above information to calculate SSxy, SSyy, and SSxx. b) Use the quantities in a) above to calculate β̂₁ c) Calculate SSE and use it to calculate the estimated standard error of β̂₁, s_β̂₁. d) Test H₀: β₁ = 0 against Hₐ: β₁ ≠ 0 at α = 0.05 level of significance.
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The exercise involving data in this and subsequent sections were designed to be solved using Excel. The following estimated regression equation based on 10 observations was presented: ŷ = 29.1270 + 0.5906x1 + 0.4980x2. Here SST = 6,724.125, SSR = 6,216.375, s_b1 = 0.0813, and s_b2 = 0.0567. a. Compute MSR and MSE (to 3 decimals). MSR = MSE = b. Compute the F test statistic (to 2 decimals). Use F table. What is the p-value? At α = .05, what is your conclusion? c. Compute the t test statistic for the significance of β1 (to 2 decimals). Use t table. The p-value is ________. At α = .05, what is your conclusion? d. Compute the t test statistic for the significance of β2 (to 2 decimals). Use t table. The p-value is ________. At α = .05, what is your conclusion?
In exercise $1,$ the following estimated regression equation based on 10 observations was presented. $$\hat{y}=29.1270+.5906 x_{1}+.4980 x_{2}$$ Here SST $=6724.125,$ SSR $=6216.375, s_{b_{1}}=.0813,$ and $s_{b_{2}}=.0567$ $\begin{array}{l}{\text { a. Compute MSR and MSE. }} \\ {\text { b. Compute } F \text { and perform the appropriate } F \text { test. Use } \alpha=.05} \\ {\text { c. Perform at test for the significance of } \beta_{1} . \text { Use } \alpha=.05} \\ {\text { d. Perform a } t \text { test for the significance of } \beta_{2} . \text { Use } \alpha=.05}\end{array}$
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