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.
Your answer appears to be the same as the book (except you are missing the "x" with .07). The difference is you rounded to two places, instead of three.
For d), substitute 32 for x into the regression equation and solve for predicted y.
I hope this helps.
To calculate the regression equation, we can use the least squares method. The equation takes the form:
y = a + bx
Where:
- y is the dependent variable (number of days in the hospital)
- x is the independent variable (age)
- a is the y-intercept
- b is the slope
To find the slope (b), we can use the formula:
b = (n∑xy - (∑x)(∑y))/(n∑x^2 - (∑x)^2)
And to find the y-intercept (a), we can use the formula:
a = (∑y - b(∑x))/n
Where:
- n is the number of data points
- ∑x represents the sum of all x values
- ∑y represents the sum of all y values
- ∑xy represents the sum of the product of each x and y value
- ∑x^2 represents the sum of the squares of all x values
Using the given data, we can calculate the necessary sums as follows:
∑x = 40 + 36 + 30 + 27 + 24 = 157
∑y = 11 + 9 + 10 + 5 + 12 = 47
∑xy = (40*11) + (36*9) + (30*10) + (27*5) + (24*12) = 1428
∑x^2 = (40^2) + (36^2) + (30^2) + (27^2) + (24^2) = 6424
n = 5
Now we can substitute these values into the formulas to find the slope (b) and the y-intercept (a):
b = (5*1428 - (157*47))/(5*6424 - (157^2))
b = (7140 - 7379)/(32120 - 24649)
b = -239/7471
b ≈ -0.032
a = (47 - (-0.032)*(157))/5
a = (47 + 5.024)/5
a ≈ 10.005
Therefore, the regression equation using these calculations is:
y ≈ 10.005 - 0.032x
Now to solve part d, we substitute x = 32 into the equation:
y ≈ 10.005 - 0.032(32)
y ≈ 10.005 - 1.024
y ≈ 8.981
Based on this prediction, a patient who is 32 years old is estimated to have a length of stay of approximately 8.981 days in the hospital. However, whether this prediction is reliable or not depends on certain factors. Since the value of r is only 0.16 and the correlation seems weak, it suggests that age alone may not be a strong predictor of the number of days in the hospital. Other variables may need to be considered to make a more accurate prediction.