The table below shows the height (in inches) and weight (in pounds) of eight basketball players.
Height
67
69
70
72
74
74
78
79
Weight
183
201
206
220
226
240
253
255
276.1 lb 276.1 lb 289.3 lb 289.3 lb 298.4 lb 298.4 lb 307.7 lb
It seems that there are four missing weight values in the table.
The table below shows the height (in inches) and weight (in pounds) of eight basketball players. Height 67 69 70 72 74 74 78 79 Weight 183 201 206 220 226 240 253 255 About how many pounds would you expect a basketball player to weigh if his height is 84 inches? Find a line of best fit for this data and use it to make your prediction. (1 point)
To find a line of best fit for this data, we can use linear regression. Using the given height and weight data, we can calculate the equation of the line using statistical software or a calculator.
Based on the table provided, we can calculate the equation of the line of best fit using the least squares method:
The mean height (x̄) is (67 + 69 + 70 + 72 + 74 + 74 + 78 + 79)/8 = 72.625
The mean weight (ȳ) is (183 + 201 + 206 + 220 + 226 + 240 + 253 + 255)/8 = 227.375
Using the formula for the slope of the regression line: b = Σ[(x - x̄)(y - ȳ)] / Σ[(x - x̄)^2]
Calculating the numerator separately:
(67-72.625)(183-227.375) + (69-72.625)(201-227.375) + (70-72.625)(206-227.375) + (72-72.625)(220-227.375) + (74-72.625)(226-227.375) + (74-72.625)(240-227.375) + (78-72.625)(253-227.375) + (79-72.625)(255-227.375) = -937.25 - 409.25 - 476.875 - 36 - 9.75 + 197.625 + 677.9375 + 167.1875 = 169.8125
Calculating the denominator separately:
(67-72.625)^2 + (69-72.625)^2 + (70-72.625)^2 + (72-72.625)^2+ (74-72.625)^2 + (74-72.625)^2 + (78-72.625)^2 + (79-72.625)^2 = 41.140625 + 10.015625 + 4.390625 + 0.390625 + 1.390625 + 1.390625 + 16.140625 + 18.515625 = 93.375
b = 169.8125 / 93.375 = 1.8209 (approximately)
Using the formula for the equation of the regression line: y = ȳ + b(x - x̄), where y is the predicted weight for a given height x.
The equation of the line is y = 227.375 + 1.8209(x - 72.625)
Now, we can use this equation to predict the weight of a basketball player with a height of 84 inches:
x = 84
y = 227.375 + 1.8209(84 - 72.625)
y = 227.375 + 1.8209(11.375)
y = 227.375 + 20.69
y ≈ 248.065
Therefore, we would expect a basketball player with a height of 84 inches to weigh approximately 248.065 pounds.