Question

Barium-137m is a radioactive form of the element barium that decays very rapidly. It is easy and safe to use for lab experiments in schools and colleges. In a typical experiment, the radioactivity of a sample of barium-137m is measured for one minute. It is then measured for three additional one-minute periods, separated by two minutes. So data are recorded at 1, 3, 5, and 7 minutes after the start of the first counting period. The measurement units are counts. Here are the data for one of these experiments.

Time 1 3 5 7
Count 577 318 204 117
a. Using the least-squares regression equation
count = 602.8 − (74.7 ✕ time)
and the observed data, find the residuals for the counts. (Round your answers to one decimal place.)
Time 1 3 5 7
Observed Count 577 318 204 117
Predicted Count ? ? ? ?
Residual ? ? ? ?
b. Plot the residuals versus time.

Answer 1

see explaination

Explanation:

Part-A:

The predicted value of count is given by:

Count = 602.8-74.7 × time

Using the above regression equation and substituting the value of 'time' variable, we get the Predicted Count as below: see table in attachment.

From the attachment, The residual value is determined by : Predicted Count - Observed Count.

Part B;

Plot of Residual v/s Time:

See attachment