age days in hospital
40 11
36 9
30 10
27 5
24 12
a. draw a scatter diagram (completed)
b. does there appear to be a correlation between age and number days in the hospital? no Find the r value for this problem to verify your answer? R=.16
c what is the regression equation for the data? y=.07+7.35
The book has 0.065x+7.35 how did they get that answer.
d.use the equation to predict the length of stay for a patient who is 32 years old. do you beleive this predicaiton is reliable? why or why not?
I am not sure how to solve d.
To find the regression equation for the data, we can use the least squares method. The regression equation is in the form y = mx + b, where y represents the dependent variable (days in the hospital) and x represents the independent variable (age).
Step 1: Calculate the mean of the age (x) and the dependent variable (y).
mean(x) = (40 + 36 + 30 + 27 + 24) / 5 = 31.4
mean(y) = (11 + 9 + 10 + 5 + 12) / 5 = 9.4
Step 2: Calculate the deviations of x and y from their means for each data point.
(x - mean(x)) (y - mean(y))
40 - 31.4 = 8.6 11 - 9.4 = 1.6
36 - 31.4 = 4.6 9 - 9.4 = -0.4
30 - 31.4 = -1.4 10 - 9.4 = 0.6
27 - 31.4 = -4.4 5 - 9.4 = -4.4
24 - 31.4 = -7.4 12 - 9.4 = 2.6
Step 3: Calculate the sum of the product of the deviations of x and y.
Σ[(x - mean(x)) * (y - mean(y))]
= (8.6 * 1.6) + (4.6 * -0.4) + (-1.4 * 0.6) + (-4.4 * -4.4) + (-7.4 * 2.6)
= 13.76 - 1.84 - 0.84 + 19.36 - 19.24 = 10
Step 4: Calculate the sum of the squares of the deviations of x.
Σ(x - mean(x))^2
= (8.6)^2 + (4.6)^2 + (-1.4)^2 + (-4.4)^2 + (-7.4)^2
= 739.96 + 21.16 + 1.96 + 19.36 + 54.76 = 837.2
Step 5: Calculate the slope (m):
m = Σ[(x - mean(x)) * (y - mean(y))] / Σ(x - mean(x))^2
m = 10 / 837.2 ≈ 0.0119
Step 6: Calculate the y-intercept (b):
b = mean(y) - (m * mean(x))
b = 9.4 - (0.0119 * 31.4) ≈ 9.4 - 0.37266 ≈ 9.0273 ≈ 9.03
Therefore, the regression equation is approximately y = 0.0119x + 9.03.
For part (d), you can substitute x = 32 into the regression equation to predict the length of stay for a patient who is 32 years old:
y = 0.0119(32) + 9.03
y ≈ 9.4098
So the predicted length of stay for a patient who is 32 years old is approximately 9.41 days. Whether this prediction is reliable or not depends on several factors. If the correlation coefficient (r) is close to 1 or -1, it indicates a strong linear relationship between age and days in the hospital, making the prediction more reliable. However, in this case, the correlation coefficient (r) is 0.16, suggesting a weak relationship. Therefore, the prediction may not be very reliable and should be interpreted with caution.