Problem 4.15

An experiment was conducted to study the toxic action of a certain chemical on silkworm larvae. The relationship of log ₁₀ (survival time) to log ₁₀ (dose) and log ₁₀ (larvae weight) was investigated. The data, obtained by feeding each larvae a precisely measured dose of the chemical in an aqueous solution and recording the survival time until death, are given in the following table. The data are stored on the attached silkw . file.

Assume the model y = ₀ + ₁ x ₁ + ₂ x ₂ +.

1. Plot the response y versus each predictor variable. Comment on these plots.
2. Obtain the least squares estimates for and give the fitted equation.
3. Construct the ANOVA table and test for a significant linear relationship between y and the two predictor variables.
4. Which independent variable do you consider to be the better predictor of log(survival time)? What are your reasons?
5. Of the models involving one or both of the independent variables, which do you prefer, and why?

Problem 4.21

The data are given on the attached file abrasion .

The hardness and the tensile strength of rubber affect its resistance to abrasion. Thirty samples of rubber are tested for hardness and tensile strength. Each sample was subjected to steady abrasion for a certain fixed period of time, and the loss of rubber was measured.

Develop a model that relates the abrasion loss to hardness and tensile strength.

Construct scatter plots of abrasion loss against hardness and tensile strength. Fit appropriate regression models, obtain and interpret the estimates of the coefficients, calculate the ANOVA table, and discuss the adequacy of the model fit. Use your model(s) to obtain a 95% confidence interval for the mean abrasion loss for rubber with hardness 70 and tensile strength 200.

Problem 6.1

A research team studies the influence of body weight and heart weight on the kidney weigh of rats. Ten rats were selected over a range of body weights, and the following results were recorded. The data are given in the attached file called kidney

Consider the models:

y = ₀ + ₁ x ₁ +.

y = ₀ + ₂ x ₂ +.

y = ₀ + ₁ x ₁ + ₂ x ₂ +.

which of these models are appropriate? Why?

Determine if there are any unusual data points. If there are, does their removal have an effect on the fitting results for the models in (a)? If there are cases with large effects, how would you present the results to the research team?

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