Exercise 15.20 Algo (Testing for Significance) Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 13 95 47 10 108 25 17 113 50 17 179 41 5 95 52 20 175 74 7 170 36 12 118 60 13 142 76 16 212 The estimated regression equation for these data is ? = -17.70 + 2.01x1 + 4.61x2 Here SST = 15,116.1, SSR = 13,894.9, s_{b1} = 0.2569, and s_{b2} = 0.9368. a. Test for a significant relationship among x1, x2, and y. Use ? = 0.05. F = (to 2 decimals) The p-value is - Select your answer - At ? = 0.05, the overall model is - Select your answer - . b. Is ?1 significant? Use ? = 0.05 (to 2 decimals). Use t table. t = (to 2 decimals) The p-value is - Select your answer - At ? = 0.05, ?1 - Select your answer - significant. c. Is ?2 significant? Use ? = 0.05 (to 2 decimals). Use t table. t = (to 2 decimals) The p-value is - Select your answer - At ? = 0.05, ?2 - Select your answer - significant.
Added by Scott R.
Close
Step 1
- \( \text{MSR} = \frac{\text{SSR}}{k} \) - \( \text{MSE} = \frac{\text{SST} - \text{SSR}}{n - k - 1} \) Given: - \( \text{SSR} = 13,894.9 \) - \( \text{SST} = 15,116.1 \) - \( k = 2 \) (number of independent variables) - \( n = 8 \) (number of observations) \[ Show more…
Show all steps
Your feedback will help us improve your experience
Hoan Nguyen and 90 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Madhur L.
The following estimated regression equation is based on 10 observations: 29.1270 + 0.5906x1 + 0.498032. Here, SST = 6,500.625, SSR = 6,025.625, R^2 = 0.0734, and R^2 adjusted = 0.0696. a. Compute MSR and MSE (to 3 decimals): MSR = SSR / k = 6,025.625 / 2 = 3,012.812 MSE = SSE / (n - k - 1) = (SST - SSR) / (n - k - 1) = (6,500.625 - 6,025.625) / (10 - 2 - 1) = 475 / 7 = 67.857 b. Compute F and perform the appropriate F test (to 2 decimals). Use α = 0.05. Use the F table. F = MSR / MSE = 3,012.812 / 67.857 = 44.38 The p-value is . At α = 0.05, the overall model is . Perform a t test for the significance of B1 (to 2 decimals): Use α = 0.05. Use the t table: t8. The p-value is . At α = 0.05, there is relationship between y and x1. d. Perform a t test for the significance of B2 (to 2 decimals): Use α = 0.05. Use the t table: t82. The p-value is . At α = 0.05, there is relationship between y and x2.
The following estimated regression equation is based on 10 observations was presented. ŷ = 29.1270 + 0.5906x₁ + 0.4980x₂ Here SST = 6,836.875, SSR = 6,303.750, s_b₁ = 0.0708, and s_b₂ = 0.0511. a. Compute MSR and MSE (to 3 decimals). MSR = MSE = b. Compute F and perform the appropriate F test (to 2 decimals). Use α = 0.05. Use the F table. F = The p-value is less than 0.01 At α = 0.05, the overall model is significant c. Perform a t test for the significance of β₁ (to 2 decimals). Use α = 0.05. Use the t table. t_β₁ = The p-value is less than 0.01 At α = 0.05, there is a significant relationship between y and x₁. d. Perform a t test for the significance of β₂ (to 2 decimals). Use α = 0.05. Use the t table. t_β₂ = The p-value is less than 0.01 At α = 0.05, there is a significant relationship between y and x₂.
Rabia S.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Watch the video solution with this free unlock.
EMAIL
PASSWORD