Question

HT	WT	BMI
70.8	169.1	23.8
66.2	144.2	23.2
71.7	179.3	24.6
68.7	175.8	26.2
67.6	152.6	23.5
69.2	166.8	24.5
66.5	135.0	21.5
67.2	201.5	31.4
68.3	175.2	26.4
65.6	139.0	22.7
63.0	156.3	27.8
68.3	186.6	28.1
73.1	191.1	25.2
67.6	151.3	23.3
68.0	209.4	31.9
71.0	237.1	33.1
61.3	176.7	33.2
76.2	220.6	26.7
66.3	166.1	26.6
69.7	137.4	19.9
65.4	164.2	27.1
70.0	162.4	23.4
62.9	151.8	27.0
68.5	144.1	21.6
68.3	204.6	30.9
69.4	193.8	28.3
69.2	172.9	25.5
68.0	161.9	24.6
71.9	174.8	23.8
66.1	169.8	27.4
72.4	213.3	28.7
73.0	198.0	26.2
68.0	173.3	26.4
68.7	214.5	32.1
70.3	137.1	19.6
63.7	119.5	20.7
71.1	189.1	26.3
65.6	164.7	26.9
68.3	170.1	25.6
66.3	151.0	24.2

We know that body mass index (BMI) is related to both height and weight, but we don’t know the actual formula.

1. Based on the data below, perform a multi linear regression to determine this formula.

2. Is this a good approximation of the true formula or not? On what do you base your conclusion?

Answer 1

a)

The regression equation is defined as,

where Y = BMI, X1 = HT, and X2 = WT

Now, the regression analysis is done in excel by following steps

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'BMI' column, Input X Range: 'HT and WT' column then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

The regression equation is,

b)

From, the regression output summary,

Overall Significance

	F	Significance F
Regression	2450.55	4.8E-40

The significance F value is 4.8E-40 which is less than 0.05 at a 5% significance level which means the model fits the data value at the 5% significance level. Hence there is sufficient evidence to conclude that independent variables fit the model significantly.

R-Square value

From, the result summary,

R Square

0.992507

The R-square value tells, how well the regression model fits the data values. The R-square value of the model is 0.9925 which means, the model explains approximately 99.25% of the variance of the data values.

Based on this evidence we can conclude the model is a good fit. Hence this a good approximation of the true formula