Help with this stats question please

Question

Systolic blood pressure (SBP) was measured for 30 people of different ages. The results are shown in the blue cells.

Part 1 - Develop a best-fit regression line for this data. Using this line, predict the SBP for an adult of age 53.

Part 2 - Outliers are defined as being more than 2 standard deviations from the value on the regression line for the same value of x (in this case, age). Based on this criterion, identify any potential outlier(s).

Part 3 - How much would the removal of the outlier(s) from the data change the predicted SBP that you calculated in Part 1?

 

Age   SBP
17     110
19     114
20     116
21     120
25     120
29     124
34     124
36     125
39     128
39     130
42     130
42     135
44     136
45     138
45     140
46     142
47     142
47     144
48     144
50     145
53     150
56     154
56     158
59     158
63     160
64     162
65     162
67     170
67     175
69     220

Answer 1

Hi,

 

To answer this question, you will need to know the means for both variables, the standard deviations for both variables and the correlation between both variables.

These are as follows:

 

M age = 45.133

SD age = 15.294

 

M SBP = 142.533

SD SBP = 22.581

 

r = 0.902

 

If you don't know how to compute any of those, let me know.

 

Regression lines will generally take the for y = c + bx, where y is the outcome (SBP), x is the predictor (age), c is the intercept and b is the slope.

 

The formula for the slope is r*(SD SBP / SD Age) = .902*(22.581/15.294) = 1.33

The formula for the intercept is M SBP - M age * b = 142.533 - 45.133*1.33 = 82.41

 

So your regression line is y = 82.41 + 1.33*x

To find the most likely SBP when age is 53, we simply plug age into the formula:

82.41 + 1.33*53 = 152.9.

 

The rest of the questions can be solved using this information. Let me know if anything didn't make sense.