In: Statistics and Probability
A chemical reaction is run 12 times, and the temperature xi(in °C) and the yield yi(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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