our group measured… arm length- from shoulder to farthest finger tip. wrist circumference-...

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