Question

A chemical reaction is run 12 times, and the temperature x_i(in °C) and the yield y_i(in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded:

x¯=65.0, y¯=29.07,∑ni=1(xi−x¯)2=6032.0,∑ni=1(yi−y¯)2=835.42,∑ni=1(xi−x¯)(yi−y¯)=1988.8x¯=65.0, y¯=29.07,∑i=1n(xi−x¯)2=6032.0,∑i=1n(yi−y¯)2=835.42,∑i=1n(xi−x¯)(yi−y¯)=1988.8

Let β₀ represent the hypothetical yield at a temperature of 0°C, and let β₁ represent the increase in yield caused by an increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold.

Find 95% confidence intervals for β₀ and β₁. Round the answers to three decimal places.

Answer 1

Solution :- data :- Given C A chemical reaction is statistics run 12 are recorded: The Toloniny Summary following some Je = 6510 9 =29.03 help (27-5)&=6032.0 Cy; -7 J = 835.42 € 2 (xi-)) cyi-) - 1988-4 for Bol Find 95% intervals confidence Answer:- deviations S Ê standard Compute the たく BÊ -v * 3) -17-9949 (Vitet 1950) 3) 603220 S = 3.7555 The 95% confidence intervals for Bo - to-do - So I not the može sẾo) | = 7.626-C21228)(3.7555), 7-626+(2.228) 03 Scanned with ... Camscānbe 0.741, 15.993)