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?
a. 276.1 lb
b. 289.3 lb
c. 298.4 lb***
d. 307.7 lb
Sorry, I meant to say if the answer is b not c?
About how many pounds would you expect a basketball player to weigh if his height is 84 inches?
a. 276.1 lb
b. 289.3 lb***
c. 298.4 lb
d. 307.7 lb
What is the answer? Wait, I'll be back soon with the answer!
289.3 is the answer to the question!!!
Trust me!! you will be correct on the question if you put 289.3 on the semester exam test for math connection academy!!!
To estimate the weight of a basketball player with a height of 84 inches, we can use the concept of linear regression. Linear regression allows us to find a line that best fits the data points in the table.
First, we need to calculate the slope and y-intercept of the line.
1. Calculate the mean of the height and weight values:
Mean height (̄X) = (67 + 69 + 70 + 72 + 74 + 74 + 78 + 79) / 8 = 73.75 inches
Mean weight (̄Y) = (183 + 201 + 206 + 220 + 226 + 240 + 253 + 255) / 8 = 223.75 pounds
2. Calculate the sum of the products of each height and weight value, then subtract the product of the mean height and mean weight:
∑(X * Y) = (67 * 183) + (69 * 201) + (70 * 206) + (72 * 220) + (74 * 226) + (74 * 240) + (78 * 253) + (79 * 255) = 150,482
∑X = 67 + 69 + 70 + 72 + 74 + 74 + 78 + 79 = 563
∑Y = 183 + 201 + 206 + 220 + 226 + 240 + 253 + 255 = 1,784
Sum of the products: 150,482
Sum of the heights: 563
Sum of the weights: 1,784
3. Calculate the sum of the squares of each height value, then subtract the square of the mean height:
∑(X^2) = (67^2) + (69^2) + (70^2) + (72^2) + (74^2) + (74^2) + (78^2) + (79^2) = 47,117
∑(X^2) = 67^2 + 69^2 + 70^2 + 72^2 + 74^2 + 74^2 + 78^2 + 79^2 = 47,117
(∑X)^2 = (563)^2 = 316,969
Sum of the squares: 47,117
Square of the sum of heights: 316,969
4. Calculate the slope (m):
m = [(∑X * ∑Y) - (n * ∑(X * Y))] / [(∑X)^2 - (n * ∑(X^2))]
n = number of data points = 8
m = [(563 * 1,784) - (8 * 150,482)] / [(563^2) - (8 * 47,117)]
= (1,005,392 - 1,203,856) / (316,969 - 377,161)
= -198,464 / -60,192
≈ 3.2981
5. Calculate the y-intercept (b):
b = (̄Y - m * ̄X)
= (223.75 - 3.2981 * 73.75)
= (223.75 - 243.725)
≈ -19.975
Now that we have calculated the slope (m ≈ 3.2981) and y-intercept (b ≈ -19.975), we can use the equation of the line to estimate the weight for a player with a height of 84 inches.
Weight = m * Height + b
≈ 3.2981 * 84 - 19.975
≈ 276.1
Therefore, about 276.1 pounds (option a) is the estimated weight for a basketball player with a height of 84 inches.