Problemas de estadistica

Problemas bono para Tercer examen de Estadística – Verano 2012
1 | |
2 | Regression data are often coded by subtracting the mean of each variable from the values of the respective variables. Consider the following coded data: X | −3 | −2 | −1 | 0 | 1 | 2 | 3 |
Y | 9 | 4 | 1 | 2 | 1 | 4 | 7 |
(a) Construct a scatter plot of the data.(b) Does the scatter plot suggest a linearrelationship?(c) Fit a linear regression equation and then plot the residuals against Y.(d) Why does that plot have a parabolic shape?(e) What does this suggest about how the prediction equation should be modified? |
3 | An engineer is interested in calibrating a flow meter to be used on a liquid-soap production line. For the test, 10 different flow rates are fixed and the corresponding meter readingsobserved. The data are shown here. Use these data to place a 95% prediction interval on x, the actual flow rate corresponding to an instrument reading of 4.0. Flow Rate, x | Instrument Reading, y |
1 | 1.4 |
2 | 2.3 |
3 | 3.1 |
4 | 4.2 |
5 | 5.1 |
6 | 5.8 |
7 | 6.8 |
8 | 7.6 |
9 | 8.7 |
10 | 9.5 |
|
4 | A manufacturer of laundry detergent was interested in testing a new productprior to market release. One area of concern was the relationship between the height of the detergent suds in a washing machine as a function of the amount of detergent added in the wash cycle. For a standard size washing machine tub filled to the full level, the manufacturer made random assignments of amounts of detergent and tested them on the washing machine. The data appear next. Height, y |Amount, x |
28.1, 27.6 | 6 |
32.3, 33.2 | 7 |
34.8, 35.0 | 8 |
38.2, 39.4 | 9 |
43.5, 46.8 | 10 |
|
5 | Suppose a researcher is interested in examining the relationship between different concentrations of pectin (0%, 1.5%, and 3% by weight) on the firmness of canned sweet potatoes after storage in a controlled 25C environment. The sample data for six cans are shown here. y (firmness) |50.5 | 46.8 | 62.3 | 67.7 | 80.1 | 79.2 |
x (concentration of pectin) | 0 | 0 | 1.5 | 1.5 | 3.0 | 3.0 |
a. Obtain the least-squares estimates for the parameters in the model y = 0 + 1x + .b. Obtain an estimate of 2.c. Give the standard error of 1. |
6 | Postulate an equation model like that U = vmax |
7 | The following data relate biomass production of soybeans to cumulative interceptedsolar radiation over an eight-week period following emergence. Biomass production is the mean dry weight in grams of independent samples of four plants. (Data courtesy of Virginia Lesser and Dr. Mike Unsworth, North Carolina State University.) Solar Radiation | Plant Biomass |
29.7 | 16.6 |
68.4 | 49.1 |
120.7 | 121.7 |
217.2 | 219.6 |
313.5 | 375.5 |
419.1 | 570.8 |
535.9 | 648.2 |641.5 | 755.6 |
|
8 | An article in the Journal of the American Statistical Association [“Markov Chain Monte Carlo Methods for y Computing Bayes Factors: A Comparative Review” (2001, Vol. 96, pp. 1122–1132)] analyzed the tabulated data on compressive strength parallel to the grain versus resin-adjusted density for specimens of radiata pine. Compressive Strength | Density | Compressive Strength| Density |
3040 | 29.2 | 3840 | 30.7 |
2470 | 24.7 | 3800 | 32.7 |
3610 | 32.3 | 4600 | 32.6 |
3480 | 31.3 | 1900 | 22.1 |
3810 | 31.5 | 2530 | 25.3 |
2330 | 24.5 | 2920 | 30.8 |
1800 | 19.9 | 4990 | 38.9 |
3110 | 27.3 | 1670 | 22.1 |
3160 | 27.1 | 3310 | 29.2 |
2310 | 24.0 | 3450 | 30.1 |
4360 | 33.8 | 3600 | 31.4 |
1880 | 21.5 | 2850 | 26.7 |
3670 | 32.2 | 1590 | 22.1|
1740 | 22.5 | 3770 | 30.3 |
2250 | 27.5 | 3850 | 32.0 |
2650 | 25.6 | 2480 | 23.2 |
4970 | 34.5 | 3570 | 30.3 |
2620 | 26.2 | 2620 | 29.9 |
2900 | 26.7 | 1890 | 20.8 |
1670 | 21.1 | 3030 | 33.2 |
2540 | 24.1 | 3030 | 28.2 |
|
9 | The vapor pressure of water at various temperatures follows: Observation Number, i | Temperature (K) | Vapor pressure (mm Hg) |
1 | 273 | 4.6...