Question

Suppose we have two thermometers. One thermometer is very precise but is delicate and heavy (X). We have another thermometer that is much cheaper and lighter, but of unknown precision (Y). We would like to know if we can (reliably) bring the lighter thermometer with us into the field. So, we set up an experiment where we expose both thermometers to 31 different temperatures and measure the temperature with each. We get the following observations
x = 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120
y = 0.02, 3.99, 7.91, 12.03, 16.09, 20.00, 23.98, 28.09, 31.94, 36.03, 40.00, 44.05, 47.95, 52.00, 55.87, 59.90, 63.91, 67.95, 72.11, 76.02, 80.01, 84.10, 88.06, 91.74, 96.02, 99.95, 103.87, 108.01, 111.99, 116.04, 120.03
Answer all questions up to 3 decimals

Estimate the simple linear regression model and

What is the standard error of ?

What is the quantile for the margin of error of a 99.9% confidence interval for ?

What is the lower end point of that interval?

What is the upper end point of that interval?

Answer 1

Estimate the simple linear regression model and

y^ = 0.0017339 + 0.9997883 x

What is the standard error of ?

standard error = 0.07963

What is the quantile for the margin of error of a 99.9% confidence interval for ?

t for 99.9% confidence interval = 3.659

It is not clear if it wants confidence interval of slope or y^ for some specific x

i am assuming it is for slope

 confint(model,level = 0.999)  0.05 % 99.95 % (Intercept) -0.1004584 0.1039261 x 0.9983254 1.0012512

What is the lower end point of that interval?

=0.9983254

What is the upper end point of that interval?

1.0012512