Question

The following data was collected on the height (inches) and weight (pounds) of women swimmers.

Height Weight

68 132

64 108

62 102

65 115

66 128

Provide a regression analysis from the height and weight data.

Summary Output

Regression Statistics

Multiple R = 0. 9603

R Square = 0. 9223

Adjust R Square = 0. 8963

Standard Error = 4. 1231

Observations = 5

ANOVA

df SS MS F Signifcant F

Regression 1 605 605 35. 5882 0. 0094

Residual 3 51 17 Total 4 656 Coefficient Standard Error t Stat P-value Lower 95% Upper 95% Lower 95. 0% Upper 95. 0%

Intercept -240. 50 59. 9554 -4. 0113 0. 0278 -431. 3048 -49. 6952 -431. 3048 -49. 6952

Height 5. 50 0. 9220 5. 9656 0. 0094 2. 5659 8. 4341 2. 5659 8. 4341

What is the "y" intercept value of b0 coeefficient of correlation?

What is the slope value b1?

If the height of a swimmer is 63 inches, the expected weight in pounds will be?

Explain in one word why you can make the relationship of the 63 inches to weight as a prediction?

If the height of a swimmer is 70 inches, the expected weight in pounds will be?

Explain in one word why you can make the relationship of the 70 inches to weight as a prediction?

Answer 1

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Explanation:

From the given regression analysis, we can determine the answers to the questions:

The "y" intercept value of the b0 coefficient (intercept) is -240.50. This represents the estimated weight (in pounds) when the height is zero.

The slope value b1, which corresponds to the coefficient for the height variable, is 5.50. This indicates that for every one-inch increase in height, the expected weight (in pounds) increases by 5.50.

To calculate the expected weight in pounds for a swimmer with a height of 63 inches, we can use the regression equation:

Weight = b0 + b1 * Height

Weight = -240.50 + 5.50 * 63

Weight = -240.50 + 346.50

Weight ≈ 106.00 pounds

Therefore, the expected weight for a swimmer with a height of 63 inches is approximately 106.00 pounds.

The relationship of 63 inches to weight can be considered a prediction because the regression analysis provides an equation that estimates the weight based on the height of the swimmers.

To predict the expected weight in pounds for a swimmer with a height of 70 inches, we can use the regression equation again:

Weight = -240.50 + 5.50 * 70

Weight = -240.50 + 385.00

Weight ≈ 144.50 pounds

Therefore, the expected weight for a swimmer with a height of 70 inches is approximately 144.50 pounds.

The relationship of 70 inches to weight can also be considered a prediction because the regression analysis provides an equation that estimates the weight based on the height of the swimmers.