Question

2. A researcher believes that a mother’s height (X) is predictive of their baby’s birth weight (Y). The researcher collects a random sample of five babies and records their weight and their mother’s height. The data is provided in the table below.

Height in Inches (X)	X2	Weight in Pounds (Y)	Y2	XY
66	4,356	6	36	396
60	3,600	7	49	420
58	3,364	9	81	522
67	4,489	7	49	469
70	4,900	5	25	350
ΣX = 321	ΣX2 = 20,709	ΣY = 34	ΣY2 = 240	ΣXY = 2,157

2A. Create the regression equation that predicts birth weight based on mother’s height.

2B. Suppose a mother has a height of 62 inches. Estimate the weight of the baby.

2C. What is the y-intercept of the regression equation?

2D. For each unit increase in height (1 inch), how much would you predict the weight of the newborns to change?

Answer 1

Height in Inches	Weight in Pounds
66	6
60	7
58	9
67	7
70	5

The independent variable is Height in Inches, and the dependent variable is Weight in Pounds.

In order to compute the regression coefficients, the following table needs to be used:

	Height in Inches	Weight in Pounds	Height in Inches*Weight in Pounds	Height in Inches2	Weight in Pounds2
	66	6	396	4356	36
	60	7	420	3600	49
	58	9	522	3364	81
	67	7	469	4489	49
	70	5	350	4900	25
Sum =	321	34	2157	20709	240

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope mm, and the y-intercept n) are obtained as follows:

2A)

Therefore, we find that the regression equation is:

2B)

Suppose a mother has a height of 62 inches.

Weight in Pounds = 23.2321 - (0.256 * 62 )

Weight in Pounds = 23.2321 - 15.872‬

Weight in Pounds = 7.3601

2c)

y-intercept of the regression equation = 23.2321

2D)

For each unit increase in height (1 inch) the weight of the new born is decreased by 0.256 pounds.

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