1.In a physics laboratory experiment on thermal conductivity a student collected the following data:

(a) Plot these data, fit a straight line by eye, and determine its splore and intercept.

(b) By least squares fit the model Y = β₀ + β₁X + ε to these data. Plot the least

squares line Ŷ = b₀ + b₁X with the data.

(c) Compare the answers to part (a) and (b) .

2.(a) An electrical engineer obtained the following data from six randomized experiments:

Suggest a simple empirical formula to relate Y to X, assuming that the standard deviation of an individual Y value is σ = 0.5.

(b) Would your answer change if σ = 0.05 ? Why?

3.(a) Using the method of least squares, fit a straight line to the following data. What are the least squares estimators of the slope and intercept of the line?

(b) Calculate 99% confidence intervals for the slope and intercept.

(c) Comment on the data and analysis, and carry out any further analysis you think is appropriate. .

4. Fit the model Y = β₁X + β₂X² + ε to these data, which were collected in random order:

1. Plot the data.
2. Obtain least squares estimates b₁ and b₂ for the parameters β₁ and β₂.
3. Draw the curve Ŷ= b₁X + b₂X² .
4. Do you think the model is adequate? Explain your answer.

5.Using the method of least squares, an experimenter fitted the model

η = β₀ + β₁X

to the data below. It is known that σ is about 0.2. A friend suggested it would be better to fit the following model instead:

η = α + β(X – Xbar)

where Xbar is the average value of X’s.

Let a and b be the estimates of α and β.

1. Is a = b₀ ? Explain your answer.
2. Is b = b₁? Explain your answer.
3. Are the predicted values of the responses for the two models, identical at X = 40? Explain your answer.

(d) Consider the two models above, which would you recommend the experimenter use: I or II or both or neither? Explain your answer.