our group measured… arm length- from shoulder to farthest finger tip. wrist circumference-...
TRANSCRIPT
PREDICTING HEIGHTS PROJECT
INTRODUCTION
Our group measured…Arm length- From shoulder to
farthest finger tip.Wrist circumference- Wrapped tape
measure around the subject’s wrist.Lower Leg- (Had subject sit down)
From top of knee to ankle.Actual height and gender were also
collected.
60
62
64
66
68
70
72
74
76
78
Lower_Leg
15 16 17 18 19 20 21
Height = 2.68Low er_Leg + 21.2
-4
-2
0
2
4
15 16 17 18 19 20 21
Lower_Leg
Collection 1 Scatter Plot
HEIGHT VS. LOWER LEG
HEIGHT VS. LOWER LEG• Describe graph (form, direction, strength)• Give correlation value (r)
LSR line
• Interpret slope…• Interpret r-squared…• Describe residual plot (form, outliers)• Is the linear model appropriate? Use correlation,
residual plot, and original plot
GENDER VS. LOWER LEG
GenderF M
60
64
68
72
76
Lower_Leg
15 16 17 18 19 20 21
Height = 1.97Low er_Leg + 32 2
Height = 1.9Low er_Leg + 36
Collection 1 Scatter Plot
FEMALES AND LOWER LEG
FEMALES:• Describe female plot• List Female LSR line• List female correlation• List female r-squared• Describe female resid plot
and comment on fit of linear model for females
62
63
64
65
66
67
68
69
shoulder_span_across_back
12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5
female_height = 0.16shoulder_span_across_back + 62.3; r2 = 0.0035
-2
0
2
4
12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5
shoulder_span_across_back
Collection 1 Scatter Plot
MALES & LOWER LEGMALES:
• Describe male plot• List male LSR line• List male correlation• List male r-squared• Describe male resid plot
and comment on fit of linear model for males
66
68
70
72
74
shoulder_span_across_back
13 14 15 16 17
male_height = 1.32shoulder_span_across_back + 49.5; r2
-4
-2
0
2
13 14 15 16 17
shoulder_span_across_back
Collection 1 Scatter Plot
Compare male and female data
HEIGHT VS. WRIST CIRCUMFERENCE
60
62
64
66
68
70
72
74
76
78
Wrist_Circumfrence
5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6
Height = 4.53Wrist_Circumfrence + 37.8
-4
0
4
8
5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6
Wrist_Circumfrence
Collection 1 Scatter Plot
HEIGHT VS. WRIST CIRCUMFERENCE
• Describe graph (form, direction, strength)• Give correlation value (r)
HEIGHT = a + b(wrist circ)
• Interpret slope…• Interpret r-squared…• Describe residual plot (form, direction,
strength)• Is the linear model appropriate? Use
correlation, residual plot, and original plot
HEIGHT AND WRIST CIRCUMFERENCE BASED ON GENDER
• Same gender analysis as before
• See slides 5 – 8
HEIGHT VS. ARM LENGTH
60
62
64
66
68
70
72
74
76
78
Arm_Length
24 25 26 27 28 29 30 31 32
Height = 1.63Arm_Length + 22.6; r2 = 0.70
-4
0
4
Arm_Length
24 25 26 27 28 29 30 31 32
Collection 1 Scatter Plot
• Describe graph (form, direction, strength)• Give correlation value (r)
HEIGHT = a + b(arm length)
• Interpret slope…• Interpret r-squared…• Describe residual plot (form, direction,
strength)• Is the linear model appropriate? Use
correlation, residual plot, and original plot
HEIGHT AND ARM LENGTH BASED ON GENDER
• Same gender analysis as before
• See slides 5 – 8
BEST OVERALL MODEL – LOWER LEG Justify choice
BEST MODEL FOR EACH GENDER
Justify choices
OUR PREDICTED HEIGHTS
(use gender specific models) Partner #1
Lower leg measurement = 17.5 inches Height = 21.2 + 2.68(17.5) = 68.1 inches Actual Height = 64 inches Residual = 64 – 68.1 = -4.1 inches Overestimate
Partner #2 Lower leg measurement = 18 inches Height = 21.2 + 2.68(18) = 69.44 inches Actual Height = 67 inches Residual = 67 – 69.44 = -2.44 inches Overestimate
Partner #3 Lower leg measurement = 17.5 inches Height = 21.2 + 2.68(17.5) = 68.1 inches Actual Height = 71 inches Residual = 71 – 68.1 = 2.9 Underestimate
PREDICTED TEACHER HEIGHTS
(use gender specific models) Mrs. McNelis
Height = 2.68(17.5) + 21.2 = 68.1 inches Mrs. Ladley
Height = 2.68(17.5) + 21.2 = 68.1 inches Mr. Smith
Height = 5.2(17) + 10.4 = 66.8 inches Mrs. Tannous
Height = 2.68(17.5) + 21.2 = 68.1 inches Miss Gemgnani
Height = 2.68(17.5) + 21.2 = 68.1 inches Mrs. Bolton
Height = 2.68(17) + 21.2 = 66.8 inches
CONFIDENCE State how confident you are in your
predictions of the guest teachers, and JUSTIFY WHY!
LINREG T TEST (ON BEST MODEL) Create linear model for best
measurement and copy onto ppt
Do lin Reg t test using the output above
Ho: β1 = 0
Ha: β1 >, <, ≠ 0
Conditions (with graphs! Do not say “see previous slides”) & statement
t = b1 – 0 = #SEb
P(t > ______|df = n—2) =
• We reject Ho….• We have sufficient evidence…• Therefore…
LIN REG CONFIDENCE INTERVAL Since we rejected Ho, we need to
complete a conf. int.
Statement
b + t*(SEb) = (____, ____)
We are 90% confident that for every 1 X variable unit increase, the Y variable increases btw ____ and ____ units on average.
ANALYSIS OF GENDER HEIGHTSSummary Stats:(do not copy this table from Fathom. Instead, type these on your slide neatly)
Collection 1
RowSummary
gender
M
gender
F
height
64.5278
18
62
63
64.25
66
68.5
1.85085
69.3561
23
65.5
68
69
71.5
73.5
2.26593
67.2364
41
62
64.5
67.5
69
73.5
3.18825
S1 = meanS2 = countS3 = minS4 = Q1S5 = medianS6 = Q3S7 = maxS8 = s
2 SAMPLE T TEST ON THE MEAN HEIGHT OF MALE/FEMALE Ho: μ males = μ femalesHa: μ males ≠ μ females
Conditions & statement
t = mean1– mean2 = s1
2 + s22
n1 n2
2* P(t > _______| df = ___) =
• We reject…..• We have sufficient evidence ….
CONFIDENCE INTERVAL If you reject Ho, complete an
appropriate confidence interval
ANALYSIS OF ARM LENGTH BY GENDER
DO NOT put this type of table on your power point!! Write out the numbers neatly.
Collection 1
RowSummary
Gender
M
Gender
F
Arm_Length
1926.26321.51262
24252628
29.5
2328.587
1.5049326
27.5283031
4227.53571.89477
2426282931
S1 = countS2 = meanS3 = sS4 = minS5 = Q1S6 = medianS7 = Q3S8 = max
2 SAMPLE T TEST ON THE MEAN ARM LENGTH OF MALE/FEMALE Ho: μ males = μ femalesHa: μ males ≠ μ females
Conditions & statement
t = mean1– mean2 = s1
2 + s22
n1 n2
2* P(t > _______| df = ___) =
• We reject…..• We have sufficient evidence ….
CONFIDENCE INTERVAL If you reject Ho, complete an
appropriate confidence interval
BIAS AND ERRORS
List and explain possible sources of bias and error in your project.
CONCLUSION Make conclusions about ALL of your
data analysis Each measurement Each test of significance and confidence interval Overall conclusion about predicting heights
Can be a bulleted list with explanation