Question

Use ALL the data found in the Excel file for your analysis. Calculate the following:

• Run the descriptive statistics for BMI (Body Mass Index) and SysBP (Systolic Blood Pressure), including graphing a scatter plot of BMI by SysBP.
• Calculate the correlation between BMI and SysBP.
• Calculate the regression with SysBP as the response variable (y) and BMI as the explanatory (sometimes called “Independent”) variable (x). In other words, we want to see how much BMI predicts SysBP. Is there a relationship between weight and blood pressure? Yes, we know there is, so we strongly suspect BMI will significantly predict SysBP. We can better understand this relationship using linear regression

BMI 28 27 33 28 29 24 34 30 36 30 31 30 38 32 27 23 26 38 32 29 26 37 24 27 33 32 33 42 30 27 42 34 24 29 28 35 41 26 35 20 28 27 40 31 45 37 35 45 29 24 28 32 34 31 30 34 30 40 36 41 30 39 36 34 38 36 39 32 28 30 25 39 25 40 21 26 24 24 31 27 29 31 24 39 31 36 21 41 23 33 26 27 26 30 23 35 52 26 35 30 47 27 30 47 23 25 32 39 28 28 35 28 32 32 30 29 32 30 27 35 36 35 44 31 31 34 25 28 29 35 37 27 28 30 24 31 38 26 32 33 31 29 38 30 38 38 36 28 31 43 24 24 31 31 36 26 30 29 35 32 24 34 39 38 35 28 38 37 33 28 25 35 33 38 36 30 28 35 31 26 64 40 32 28 45 29 25 31 34 30 35 29 33 31 22 30 38 29 35 26 41 26 28 32 28 29 27 27 32 38 31 30 27 33 28 38 37 29 25 23 38 27 39 20 29 29 25 28 39 31 35 31 39 40 30 29 37 31 33 34 25 24 42 23 42 26 34 38 38 44 26 32 30 24 31 30 24 30 31 26 42 27 24 27 28 30 24 22 28 32 44 25 31 25 24 36 27 32 25 33 28 30 33 34 36 30 30 40 29 39 27 27 31 27 36 35 23 27 24 32 24 30 29 32 29 40 31 43 36 40 33 35 38 26 28 34 47 33 25 31 34 34 30 33 33 24 28 34 29 29 35 25 40 35 29 28 31 42 38 41 27 37 38 33 40 33 32 30 41 27 25 27 34 32 39 24 32 35 24 32 31 29 33 30 32 30 26 28 31 30 27 34 23 41 30 45 25 30 30 24 38 36 44 31 30 36 47

SysBP 128 108 108 138 118 114 132 110 162 144 142 158 126 128 114 116 134 122 150 138 134 110 138 118 124 158 114 120 110 100 142 109 108 124 118 132 126 118 136 148 122 128 135 140 128 110 108 136 138 126 114 108 152 126 118 120 146 109 136 120 129 120 130 136 130 136 126 112 128 110 122 104 112 138 120 126 122 112 132 122 142 136 122 102 112 110 100 152 125 138 130 118 114 120 142 128 138 124 132 130 152 126 118 154 118 122 115 122 146 146 124 114 134 140 118 100 124 110 124 134 136 138 117 112 112 118 130 128 120 122 142 132 112 128 132 120 144 108 122 128 160 124 150 128 130 150 102 110 126 120 118 130 144 128 168 134 132 136 130 126 128 134 120 100 110 132 155 140 128 112 128 154 114 156 118 142 112 100 143 124 114 132 124 114 120 130 118 98 120 158 118 124 140 124 126 140 122 126 132 116 122 112 108 136 122 124 122 150 128 142 98 126 116 112 114 136 138 142 138 130 122 120 124 108 118 128 122 118 126 136 134 120 136 120 142 118 124 136 134 134 118 114 120 126 120 118 112 110 130 124 108 114 122 113 112 108 108 124 132 108 134 104 122 114 118 114 118 164 116 126 130 120 120 122 132 106 124 142 110 144 136 118 112 128 130 128 120 146 136 124 148 116 132 124 116 136 128 127 120 112 112 130 107 134 118 112 110 164 128 136 108 130 112 122 116 130 126 120 124 120 112 132 118 120 148 118 124 148 140 110 115 114 136 158 122 120 108 134 138 122 130 118 138 118 118 136 118 140 120 108 106 120 120 134 122 112 130 120 112 120 126 120 134 118 130 104 100 120 122 120 96 124 104 112 128 138 100 136 120 118 128 118 128 115 120 132 118

Answer 1

a) Descriptive statistics

BMI		SysBP
Mean	31.73643	Mean	124.9922
Standard Error	0.297813	Standard Error	0.660356
Median	31	Median	124
Mode	30	Mode	120
Standard Deviation	5.85868	Standard Deviation	12.99073
Sample Variance	34.32414	Sample Variance	168.759
Kurtosis	1.973721	Kurtosis	0.331616
Skewness	0.896971	Skewness	0.541162
Range	44	Range	72
Minimum	20	Minimum	96
Maximum	64	Maximum	168
Sum	12282	Sum	48372
Count	387	Count	387
Confidence Level(95.0%)	0.58554	Confidence Level(95.0%)	1.298345

Scatter Plot

Correlation matrix

	BMI	SysBP
BMI	1
SysBP	0.1986	1

correlation between SysBP and BMI = 0.1968 which is weak positive correlation.

Regression output

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.198626
R Square	0.039452
Adjusted R Square	0.036957
Standard Error	12.74842
Observations	387
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2569.958	2569.958	15.81297	8.35E-05
Residual	385	62571.02	162.5221
Total	386	65140.98
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	111.0148	3.574203	31.06002	6.5E-107	103.9874	118.0422	103.9874	118.0422
BMI	0.440423	0.110755	3.976553	8.35E-05	0.222662	0.658183	0.222662	0.658183

From the ANOVA table we get p-value is < 0.001, hence we reject null hypothesis and conclude that Yes, we know there is, so we strongly suspect BMI will significantly predict SysBP. We can better understand this relationship using linear regression.