Question

Hello,

Q1: where does the f(1,17) the 1 come from?

Q2, how do i get the second equation from the first equation?

thanks

Heat treating is often used to carburize metal parts such as gears. The thickness of the carburized layer is considered an important feature of the gear, and it contributes to the overall reliability of the part. Because of the critical nature of this feature, a lab test is performed on each furnace load. The test is a destructive one, where an actual part is cross sectioned and soaked in chemical for a period of time. This test involves running a carbon analysis on the surface of both the gear pitch (top of the gear tooth) and the gear root (between the gear teeth). The data below are the results of the pitch carbon-analysis test for 19 parts. Soak Time 058 Pitch 0.013 0,016 0.015 0.016 0,015 0,016 0.014 0.021 Soak Time Pitch 0.021 0,66 0,66 0,66 0,66 0,66 1.00 1.17 1.17 1.20 2.00 0.019 0,021 0,025 0.025 2.00 0,026 0.024 2.20 1.17 2.2 0.025 0.024 2.20 0.019 1.17 (a) Fit a simple linear regression relating the pitch carbon analysis y against soak time. Test Ho 31= 0 (b) If the hypothesis in part (a) is rejected, determine if the linear model is adequate Step-by-step solution Step 1 of 6 A From the given data, we have Soak Time Pitch X Y у х.у, х, 0.013 0.336 0.000169 0,007540 0.58 0.016 0.436 0.000256 0.010560 0.66 0.66 0.015 0.436 0.000225 0.009900 0 66 0.016 0.436 0.000256 0.010560 0 66 0.015 0.436 0.000225 0.009900 0.66 n 016 А2с 0.026 4.000 0.000676 0.052000 2.00 0.024 4,840 0.000576 0,052800 2.20 0.025 4.840 0.000625 0.055000 2.20 0.024 4.840 0.000576 0.052800 2.20 From the above table, Σ- X = 35.6878, 0.373,y =0.007655 n=19, S X, = 23.7, X,Y = 0.50485 and (a) Simple linear regression model Hi=B+ B,x Then the least squares estimates b, and b for the regress ion coefficients B and B are obtained by b, 19x 0.50485-(23.7 x 0.373) 19x35.6878-(23.7) 0.75205 116.3782 b0.006462 Comment Step 2 of 6 And ΣΣ-Σx b n 0.373-(0.006462 x 23.7) 19 b=0.011571 Therefore, the fitted linear regression relating the pitch carbon analysis y against soak time x is 0.011571+ 0.006462x Null hypothesis, Alternative hypothesis, H B0 Let the level of significance be a 0.05 from Table6, foos (1,17) = 4.45 Comment Step 3 of 6 Then the test statistic SSR/1 SSE /(n-2) SSR Where SSR b,S Sy-b,S 2 n- nil (23.7 x 0.373) 19 =0.50485 ST=0.039582 Comment Step 4 of 6 (3-- 0.007655 (0.373) 19 S 0.000332 Comment Then the test statistic SSR/1 SSE/(n-2 SSR S2 Where SS Syy-b,S n-2 X (23.7 xi 7x0.373) =0.50485 S0.039582 Comment Step 4 of 6 (137-A3- (0373 =0,007655 19 0.000332 Comment Step 5 of 6 A Therefore, SSR =0.006462 x 0.039582 = 0.000256 0.000332-(0.006462 x 0.039582) 17 S2 =0,000004

Answer 1

Here there are 2 parameters (soak time and pitch). So, number of independent parameters=p-1=2-1=1

Hence, we get f(1,7).

Also, SSE/n-2= s^{​​​​​​2}​​​. So, the formula becomes f=SSR/S^2