he 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 a line of best fit for the given data, we can use linear regression. Linear regression is a statistical method used to find the relationship between two variables, in this case, height and weight.
Using the given data, we can calculate the equation of the line of best fit. Here are the steps:
1. Calculate the mean (average) of the height and weight:
Mean height = (67 + 69 + 70 + 72 + 74 + 74 + 78 + 79) / 8 = 72.625 inches
Mean weight = (183 + 201 + 206 + 220 + 226 + 240 + 253 + 255) / 8 = 222.625 pounds
2. Calculate the deviations from the mean for both height and weight:
Deviation of height = height - mean height
Deviation of weight = weight - mean weight
For example:
For the first data point (67, 183), the deviation of height = 67 - 72.625 = -5.625 inches
deviation of weight = 183 - 222.625 = -39.625 pounds
3. Calculate the product of the deviations for each data point:
Product of deviation = deviation of height * deviation of weight
For example:
For the first data point, the product of deviation = (-5.625) * (-39.625) = 223.828125
4. Calculate the sum of the products of deviation:
Sum of product of deviation = Sum of (deviation of height * deviation of weight)
For all data points:
Sum of product of deviation = Sum of (Product of deviation)
5. Calculate the square of the deviations of height:
Square of deviation of height = (deviation of height)^2
For example:
For the first data point, the square of the deviation of height = (-5.625)^2 = 31.640625
6. Calculate the sum of the square of the deviations of height:
Sum of square of deviation of height = Sum of (square of deviation of height)
For all data points:
Sum of square of deviation of height = Sum of (Square of deviation of height)
7. Calculate the slope of the line of best fit:
Slope = Sum of product of deviation / Sum of square of deviation of height
8. Calculate the y-intercept of the line of best fit:
y-intercept = mean weight - (slope * mean height)
9. Write the equation of the line of best fit:
y = slope * x + y-intercept
where x represents the height and y represents the weight.
Using the calculated equation of the line of best fit, we can then predict the weight of a basketball player with a height of 84 inches.