In: Math
What is the error of the predicted Systolic BP when Age = 39?
Age | Systolic BP | Year | Stories | Height | Year | Germany GDP | ||
47 | 145 | 1990 | 54 | 770 | 1950 | 5.725433 | ||
65 | 162 | 1980 | 47 | 677 | 1951 | 6.256754 | ||
46 | 142 | 1990 | 28 | 428 | 1952 | 6.70308 | ||
67 | 170 | 1989 | 38 | 410 | 1953 | 7.256435 | ||
42 | 124 | 1966 | 29 | 371 | 1954 | 7.72644 | ||
67 | 158 | 1976 | 38 | 504 | 1955 | 8.570349 | ||
56 | 154 | 1974 | 80 | 1136 | 1956 | 9.076571 | ||
64 | 162 | 1991 | 52 | 695 | 1957 | 9.45931 | ||
56 | 150 | 1982 | 45 | 551 | 1958 | 9.665697 | ||
59 | 140 | 1986 | 40 | 550 | 1959 | 10.259906 | ||
34 | 110 | 1931 | 49 | 568 | 1960 | 10.608815 | ||
42 | 128 | 1979 | 33 | 504 | 1961 | 11.032132 | ||
48 | 130 | 1988 | 50 | 560 | 1962 | 11.384714 | ||
45 | 135 | 1973 | 40 | 512 | 1963 | 11.611703 | ||
17 | 114 | 1981 | 31 | 448 | 1964 | 12.266443 | ||
20 | 116 | 1983 | 40 | 538 | 1965 | 12.813883 | ||
19 | 124 | 1968 | 27 | 410 | 1966 | 13.016213 | ||
36 | 136 | 1927 | 31 | 409 | 1967 | 12.964814 | ||
50 | 142 | 1969 | 35 | 504 | 1968 | 13.730252 | ||
39 | 120 | 1988 | 57 | 777 | 1969 | 14.665157 | ||
21 | 120 | 1987 | 31 | 496 | 1970 | 15.392277 | ||
44 | 160 | 1960 | 26 | 386 | 1971 | 15.720841 | ||
53 | 158 | 1984 | 39 | 530 | 1972 | 16.197464 | ||
63 | 144 | 1976 | 25 | 360 | 1973 | 16.907173 | ||
29 | 130 | 1920 | 23 | 355 | 1974 | 16.97702 | ||
25 | 125 | 1931 | 102 | 1250 | 1975 | 16.72403 | ||
69 | 175 | 1989 | 72 | 802 | 1976 | 17.6721 | ||
1907 | 57 | 741 | 1977 | 18.195684 | ||||
1988 | 54 | 739 | 1978 | 18.798212 | ||||
1990 | 56 | 650 | 1979 | 19.640699 | ||||
1973 | 45 | 592 | 1980 | 19.935295 | ||||
1983 | 42 | 577 | 1981 | 19.903635 | ||||
1971 | 36 | 500 | 1982 | 19.723139 | ||||
1969 | 30 | 469 | 1983 | 19.985983 | ||||
1971 | 22 | 320 | ||||||
1988 | 31 | 441 | ||||||
1989 | 52 | 845 | ||||||
1973 | 29 | 435 | ||||||
1987 | 34 | 435 | ||||||
1931 | 20 | 375 | ||||||
1931 | 33 | 364 | ||||||
1924 | 18 | 340 | ||||||
1931 | 23 | 375 | ||||||
1991 | 30 | 450 | ||||||
1973 | 38 | 529 | ||||||
1976 | 31 | 412 | ||||||
1990 | 62 | 722 | ||||||
1983 | 48 | 574 | ||||||
1984 | 29 | 498 | ||||||
1986 | 40 | 493 | ||||||
1986 | 30 | 379 | ||||||
1992 | 42 | 579 | ||||||
1973 | 36 | 458 | ||||||
1988 | 33 | 454 | ||||||
1979 | 72 | 952 | ||||||
1972 | 57 | 784 | ||||||
1930 | 34 | 476 | ||||||
1978 | 46 | 453 | ||||||
1978 | 30 | 440 | ||||||
1977 | 21 | 428 | ||||||
Here is the data for Age vs Systolic BP
Let us run a regression on this and predict Systolic BP given age
Systolic BP = f(Age)
The regression output is as follows-
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.850680578 | |||||||
R Square | 0.723657446 | |||||||
Adjusted R Square | 0.712603744 | |||||||
Standard Error | 9.726507714 | |||||||
Observations | 27 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1 | 6193.542859 | 6193.542859 | 65.46742752 | 1.90987E-08 | |||
Residual | 25 | 2365.123808 | 94.60495231 | |||||
Total | 26 | 8558.666667 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 96.36177647 | 5.682961824 | 16.95625969 | 3.18944E-15 | 84.6574975 | 108.0660554 | 84.6574975 | 108.0660554 |
X Variable 1 | 0.95848899 | 0.118460753 | 8.091194443 | 1.90987E-08 | 0.714514502 | 1.202463479 | 0.714514502 | 1.202463479 |
From the above, we have Systolic BP = 96.36 + 0.958*Age
Predicted Systolic BP for Age = 39 is 96.36 + 0.958*39 = 133.72
As per the data, for Age=39, Systolic BP = 120
Error = Actual-Predicted = 120-133.72 = -13.72
Let me know if you need anything else, if not please don't forget to like the answer :)