10-8. Exercises

EXERCISES

The exercises in this section are unrelated to those in previous sections.

Ex 1. The data give the amount x of silicofluoride in the water (mg/L) and the amount y of lead in the bloodstream (μg/dL) of ten children in various communities with and without municipal water. Perform a complete analysis of the data, in analogy with the discussion in this section (that is, make a scatter plot, do preliminary computations, find the least squares regression line, find $SSE$, $s_ε$ , and $r$ , and so on). In the hypothesis test use as the alternative hypothesis $β_1>0$ , and test at the 5% level of significance. Use confidence level 95% for the confidence interval for $β_1$ . Construct 95% confidence and predictions intervals at $x_p=2$ at the end. x 0.0 0.0 1.1 1.4 1.6 y 0.3 0.1 4.7 3.2 5.1 x 1.7 2.0 2.0 2.2 2.2 y 7.0 5.0 6.1 8.6 9.5

Ex 2. The table gives the weight $x$ (thousands of pounds) and available heat energy $y$ (million BTU) of a standard cord of various species of wood typically used for heating. Perform a complete analysis of the data, in analogy with the discussion in this section (that is, make a scatter plot, do preliminary computations, find the least squares regression line, find $SSE$, $s_ε$, and $r$, and so on). In the hypothesis test use as the alternative hypothesis $β_1>0$ , and test at the 5% level of significance. Use confidence level 95% for the confidence interval for $β_1$ . Construct 95% confidence and predictions intervals at $x_p=5$ at the end. x 3.37 3.50 4.29 4.00 4.64 y 23.6 17.5 20.1 21.6 28.1 x 4.99 4.94 5.48 3.26 4.16 y 25.3 27.0 30.7 18.9 20.7

LARGE DATA SET EXERCISES

16KB

data3.xls

Data Set 3

23KB

data3A.xls

Data Set 3A

Ex 3. Large Data Sets 3 and 3A list the shoe sizes and heights of 174 customers entering a shoe store. The gender of the customer is not indicated in Large Data Set 3. However, men’s and women’s shoes are not measured on the same scale; for example, a size 8 shoe for men is not the same size as a size 8 shoe for women. Thus it would not be meaningful to apply regression analysis to Large Data Set 3. Nevertheless, compute the scatter diagrams, with shoe size as the independent variable ($x$) and height as the dependent variable ($y$), for (i) just the data on men, (ii) just the data on women, and (iii) the full mixed data set with both men and women. Does the third, invalid scatter diagram look markedly different from the other two?

Ex 4. Separate out from Large Data Set 3A just the data on men and do a complete analysis, with shoe size as the independent variable ($x$) and height as the dependent variable ($y$). Use $α=0.05$ and $x_p=10$ whenever appropriate.

Ex 5. Separate out from Large Data Set 3A just the data on women and do a complete analysis, with shoe size as the independent variable ($x$) and height as the dependent variable ($y$). Use $α=0.05$ and $x_p=10$ whenever appropriate.