A chemical reaction is run 12 times, and the temperature xi(in °C) and the yield yi(in...

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¯=29.06

∑ni=1(xi−x¯)2=6032.0

∑ni=1(yi−y¯)2=835.42

∑ni=1(xi−x¯)(yi−y¯)=1988.5x¯=65.0,

y¯=29.06,∑i=1n(xi−x¯)2=6032.0,

∑i=1n(yi−y¯)2=835.42,

∑i=1n(xi−x¯)(yi−y¯)=1988.5

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.

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