Midterm 2Biometry 333Fall 2006Name:______
You are allowed a calculator, clean probability tables, Minitab, R, a 3-by-5 inch note card of notes. No use of neighbors or internet is allowed.
Show all work. Ask the instructor if a question is not clear.
Each problem is worth 4 points.
(1) DDT levels were measured in falcons captured at nesting sites in the US, Canada, and near the Arctic. The age of the falcons were also recorded as young, old, or middle-aged. The word formula for the fitted model was DDT = NESTING + AGE.
(1a) What is the coefficient value for “young” falcons? Show your work.
(1b) What is the expected DDT level of the “old” falcons found at Arctic nest sites?
(1c) Was there a statistically significant difference in mean levels of DDT between different nesting sites? (Yes or No.) Very specifically explain how you reached your decision.
(1d) One of the F-statistics in the ANOVA table has been replaced by FFFFF. Calculate the F-statistic that belongs in the place of FFFFF.
(1e) The fitted model was DDT = NESTING + AGE + N(0,), where N(0,) is the normally distributed error term. Estimate the standard deviation and explain how you derived your answer.
(1f) Which falcons have the greatest DDT concentrations?
(1g) The adjusted mean squares for NESTING was replaced by AAAAAA. Calculate the value for AAAAAA. Show your work.
(1h) If an interaction model DDT = NESTING|AGE were fit, how many degrees of freedom would the NESTING*AGE interaction component of the model use?
(2) The weight, height, gender, and brain size (kilopixel count from MRIs) were measured on volunteer college students. The word formula for the fitted model is: kilopixel = Height + Weight + Gender.
(2a) In kilopixels, what is the expected difference in brain sizes between men and women of the same height and weight? Which gender has the greater kilopixel count? Show your work.
(2b) Calculate the R-square value for this model. Show your work.
(2c) A female weighed 140 pounds and was 68 inches tall. Calculate her expected kilopixel count.
(2d) The p-value for Gender has been replaced with XXXXX in the ANOVA table. Calculate the p-value. Show your work.
(2e) Calculate a 95% confidence interval for the Height coefficient. Show your work.
(2f) Calculate the t-statistic and p-value for the Weight coefficient. They have been replaced by TTTT and YYYYY in the Coefficient table. Show your work.
(2g) Write the equation for the line that represents the males and another equation that represents the females. (Have your equations in the y=a+bx format.)
(2h) For each inch increase in height, how much does the expected kilopixel count increase(decrease)?
(2i) What would be the sum of squares error for the model with the word formula: kilopixel=Height + Gender? Show your work.
(3) The systolic blood pressure (mm Hg), age (years), and calf skin fold (mm, a measure of body fat) were measured on Peruvian men. Age, calf skin fold, and their interaction were used to predict blood pressure. The word formula for the fitted model was Systol=Age|Calf.
(3a) A man aged 32 years had a calf skin fold of 6mm. Calculate his predicted blood pressure. Show your work.
(3b) Explain how the total sum of squares, 6531.4, was calculated. Be very specific. (You do not have the information available to actually do the calculation.)
(3c) Calculate the sum of squares error for the model: ? Show your work.
(4) Various characteristics of flowering trillium plants were measured: leaf length (cm), stem length (cm), and flower type (p=pink, s=seeded, or w=white). Leaf length, flower type, and their interaction were used to predict stem length. The word formula for the fitted model was: stem = leaf|flower.
(4a) Provide the equations for the predicted stem length when given the leaf length for each of the three flower types. (Use the line equation y=a+bx format.)
(4b) Test whether the leaf coefficient is equal to 0.4. Show your work and provide a p-value.
(5) In general, explain how the sum of squares error for a model is calculated.
(6) Suppose you have a model: .
(6a) In general, how is the sequential sum of squares calculated for?
(6b) In general, how is the adjusted sum of squares calculated for?
Problem 1
General Linear Model: DDT versus NESTING, AGE
Factor Type Levels Values
NESTING fixed 3 Arctic, Canada, US
AGE fixed 3 middleAged, old, young
Analysis of Variance for DDT, using Adjusted SS for Tests
Source DF Seq SS Adj SS Adj MS F P
NESTING 2 17785.4 17785.4 AAAAAA 2454.58 0.000
AGE 2 1721.2 1721.2 860.6 FFFFF 0.000
Error 22 79.7 79.7 3.6
Total 26 19586.3
Term Coef SE Coef T P
Constant 44.3704 0.3663 121.13 0.000
NESTING
Arctic 36.2963 0.5180 70.07 0.000
Canada -18.2593 0.5180 -35.25 0.000
AGE
middleAged -0.1481 0.5180 -0.29 0.778
old 9.8519 0.5180 19.02 0.000
Problem 2
General Linear Model: kilopixel versus Gender
Factor Type Levels Values
Gender fixed 2 Female, Male
Analysis of Variance for kilopixel, using Adjusted SS for Tests
Source DF Seq SS Adj SS Adj MS F P
Height 1 67442 3492 3492 1.12 0.297
Weight 1 3950 641 641 fffff YYYYY
Gender 1 17721 17721 17721 5.70 XXXXX
Error 34 105700 105700 3109
Total 37 194813
Term Coef SE Coef T P
Constant 603.1 225.8 2.67 0.012
Height 3.895 3.675 1.06 0.297
Weight 0.2574 0.5667 TTTT YYYYY
Gender
Female -31.87 AAAAA BBBB XXXXX
Problem 3
General Linear Model: Systol versus
Factor Type Levels Values
Analysis of Variance for Systol, using Adjusted SS for Tests
Source DF Seq SS Adj SS Adj MS F P
Calf 1 410.8 329.8 329.8 1.95 0.172
Age 1 0.3 157.8 157.8 0.93 0.341
Age*Calf 1 188.9 188.9 188.9 1.11 0.298
Error 35 5931.4 5931.4 169.5
Total 38 6531.4
Term Coef SE Coef T P
Constant 100.53 21.77 4.62 0.000
Calf 3.058 2.192 1.39 0.172
Age 0.5944 0.6160 0.96 0.341
Age*Calf -0.06660 0.06308 -1.06 0.298
Problem 4
General Linear Model: stem versus flower
Factor Type Levels Values
flower fixed 3 p, s, w
Analysis of Variance for stem, using Adjusted SS for Tests
Source DF Seq SS Adj SS Adj MS F P
leaf 1 396.610 119.879 119.879 107.96 0.000
flower 2 1.846 2.761 1.381 1.24 0.289
flower*leaf 2 2.618 2.618 1.309 1.18 0.308
Error 576 639.580 639.580 1.110
Total 581 1040.654
Term Coef SE Coef T P
Constant 0.5538 0.3735 1.48 0.139
leaf 0.31318 0.03014 10.39 0.000
flower
p 0.3457 0.4309 0.80 0.423
s 0.0679 0.6927 0.10 0.922
leaf*flower
p -0.01754 0.03396 -0.52 0.606
s -0.01930 0.05648 -0.34 0.733
1