The following are data for 12 individual‟s daily sodium intake and their
systolic blood pressure readings.
Person Sodium BP
1 6.8 154
2 7.0 167 '
3 6.9 162
4 7.2 175
5 7.3 190
6 7.0 158
7 7.0 166
8 7.5 195
9 7.3 189
10 7.1 186
11 6.5 148
12 6.4 140
A researcher investigator is interested in learning how strong
the association is between these variables and how well we can
predict blood pressure from sodium intake.
a. Calculate the value of r and the regression equation for the data
b. What would be a likely blood pressure for a person with sodium of
6.3? How about sodium of 7.6?
"\\bar{Y}=\\dfrac{1}{n}\\sum_iY_i=\\dfrac{2030}{12}=169.16666666667"
"SS_{XX}=\\sum_i(X_i-\\bar{X})^2=1.1400000000001"
"SS_{YY}=\\sum_i(Y_i-\\bar{Y})^2=3531.6666666667"
"SS_{XY}=\\sum_i(X_i-\\bar{X})(Y_i-\\bar{Y})=59.800000000001"
"m=slope=\\dfrac{SS_{XY}}{SS_{XX}}"
"=\\dfrac{59.800000000001}{1.1400000000001}=52.45614"
"n=\\bar{Y}-m\\bar{X}"
"=169.16666666667-52.45614(7)"
"=\u2212198.02632"
Therefore, we find that the regression equation is:
Correlation coefficient:
"=0.94245127"
a. "r=0.94245127"
We have strong positive correlation.
The regression equation is:
b.
"=132.447362"
Systolic blood pressure readings are "132.447362."
c.
"=200.640344"
Systolic blood pressure readings are "200.640344."
Comments
Leave a comment