For the men age 18 and over the avg height was 69 inches with an SD of 3 inches and avg weight was 190 lbs with an SD of 42 pounds. the r value is around 0.41. Estimate the average weight of the men whose heights were 66in, 24 in, and 0in.
Let's gather the data:
Height (x): mean = 69, sd = 3
Weight (y): mean = 190, sd = 42
Correlation: r = 0.41
Regression equation is in this format:
predicted y = a + bx
...where a = intercept and b = slope.
To find the equation, you need to substitute the information given in the problem into a workable formula:
predicted y = (rSy/Sx)X - (rSy/Sx)xbar + ybar
...where r = correlation, Sy = sd of y, Sx = sd of x, and X is the variable in 'a + bx' equation.
Note: xbar = mean of x; ybar = mean of y.
Therefore: predicted y = [(0.41)(42)/(3)]X - [(0.41)(42)/(3)]69 + 190 = 5.74X - 206.06
predicted y = -206.06 + 5.74x
Check the math, then substitute the weights given for x, solving for predicted y.
I hope this will help.
To estimate the average weight of men whose heights are given as 66 inches, 24 inches, and 0 inches, we first need to understand the correlation between height and weight for this population.
In this case, the r value of approximately 0.41 indicates a moderate positive correlation between height and weight. This means that, on average, taller men tend to weigh more.
To estimate the average weight for the given heights, we can use the correlation to calculate predicted weights using the regression equation:
Predicted Weight = b * Height + a
In this equation, b represents the slope of the regression line (which is given by the correlation coefficient multiplied by the standard deviation of the weight divided by the standard deviation of the height), and a represents the intercept of the regression line (which is given by the average weight minus the slope multiplied by the average height).
Let's calculate the components and proceed with the estimation:
1. Calculate the slope (b):
b = r * (SD of weight / SD of height)
b = 0.41 * (42 lbs / 3 inches) ~ 5.73 lbs/inch
2. Calculate the intercept (a):
a = avg weight - b * avg height
a = 190 lbs - 5.73 lbs/inch * 69 inches ~ 19.38 lbs
3. Estimate the average weight for each given height:
For a height of 66 inches:
Predicted Weight = b * Height + a
Predicted Weight = 5.73 lbs/inch * 66 inches + 19.38 lbs
Predicted Weight ≈ 378 lbs
For a height of 24 inches:
Predicted Weight = b * Height + a
Predicted Weight = 5.73 lbs/inch * 24 inches + 19.38 lbs
Predicted Weight ≈ 159 lbs
For a height of 0 inches:
Predicted Weight = b * Height + a
Predicted Weight = 5.73 lbs/inch * 0 inches + 19.38 lbs
Predicted Weight ≈ 19.38 lbs
Therefore, the estimated average weight for men with heights of 66 inches, 24 inches, and 0 inches are approximately 378 lbs, 159 lbs, and 19.38 lbs, respectively.