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) Responses 276.1 lb 276.1 lb 289.3 lb 289.3 lb 298.4 lb 298.4 lb 307.7 lb
To find the line of best fit for the data, we can use a linear regression model. This will allow us to predict the weight of a basketball player based on their height.
Using the given height and weight data, we can calculate the equation of the line of best fit.
First, we need to find the slope (m) and y-intercept (b) of the line.
We can use the formula for the slope of a line:
m = (Σ(xy) - (Σx)(Σy) / n(Σx^2) - (Σx)^2)
where Σxy is the sum of the products of each height and weight,
Σx is the sum of all the heights,
Σy is the sum of all the weights,
and Σx^2 is the sum of the squares of all the heights.
Calculating each of these values, we have:
Σxy = (67*183) + (69*201) + (70*206) + (72*220) + (74*226) + (74*240) + (78*253) + (79*255)
= 1240119
Σx = 67 + 69 + 70 + 72 + 74 + 74 + 78 + 79
= 563
Σy = 183 + 201 + 206 + 220 + 226 + 240 + 253 + 255
= 1784
Σx^2 = (67^2) + (69^2) + (70^2) + (72^2) + (74^2) + (74^2) + (78^2) + (79^2)
= 39693
Substituting these values into the formula, we get:
m = (1240119 - (563)(1784)) / (8(39693 - (563)^2))
≈ -3.669
Next, we can find the y-intercept (b) using the formula:
b = (Σy - mΣx) / n
Substituting the values into the formula, we have:
b = (1784 - (-3.669)(563)) / 8
≈ 304.006
Therefore, the equation of the line of best fit is:
y = -3.669x + 304.006
To predict the weight of a basketball player with a height of 84 inches, we substitute x = 84 into the equation:
y ≈ -3.669(84) + 304.006
≈ 307.714
So, we would expect a basketball player with a height of 84 inches to weigh approximately 307.7 pounds (closest option is 307.7 lb).