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.l
To find a line of best fit for this data, we can use linear regression. We can use the variables "height" (x) and "weight" (y) to create a scatter plot and draw a line that best fits the data points.
First, let's calculate the slope and y-intercept of the line. We can use the following formulas:
mean_x = (x1 + x2 + ... + xn) / n
mean_y = (y1 + y2 + ... + yn) / n
slope = Σ((xi - mean_x)(yi - mean_y)) / Σ((xi - mean_x)^2)
y-intercept = mean_y - slope * mean_x
Using the given data, we can calculate the mean_x, mean_y, slope, and y-intercept. Let's calculate them:
height (x): 67 69 70 72 74 74 78 79
weight (y): 183 201 206 220 226 240 253 255
mean_x = (67 + 69 + 70 + 72 + 74 + 74 + 78 + 79) / 8 = 72.5
mean_y = (183 + 201 + 206 + 220 + 226 + 240 + 253 + 255) / 8 = 225.375
xi - mean_x: -5.5 -3.5 -2.5 -0.5 1.5 1.5 5.5 6.5
yi - mean_y: -42.375 -24.375 -19.375 -5.375 0.625 14.625 27.625 29.625
(xi - mean_x)^2: 30.25 12.25 6.25 0.25 2.25 2.25 30.25 42.25
Σ((xi - mean_x)(yi - mean_y)): -223.125
Σ((xi - mean_x)^2): 126.25
slope = -223.125 / 126.25 ≈ -1.7676
y-intercept = 225.375 - (-1.7676 * 72.5) ≈ 360.2081
Now that we have the slope and y-intercept, we can create the equation of the line: y = -1.7676x + 360.2081.
To find the predicted weight for a height of 84 inches, we can substitute x = 84 into the equation:
y = -1.7676 * 84 + 360.2081
y ≈ 202.3619
So, we would expect a basketball player with a height of 84 inches to weigh approximately 202 pounds.