Although the linear
regression line values are quite different, the error margins mean that there is considerable overlap between the 95 % confidence limits so the two data sets are in fact in statistical agreement.
Not exact matches
The blue and yellow dots on the
regression lines correspond to the relative valuation of the
value factor, equal to 0.13 in March 2016, comfortably in the bottom decile of historical relative valuation.
The dashed
line shows the
regression fit between the two; a lower starting valuation for
value relative to growth strongly correlates with higher subsequent five - year performance.
Perhaps it's my age (I remember when I had do do linear
regressions with a pencil and paper for the sums, and a slide rule to help with the squares and square roots), but a fundamental principle of a linear least squares
regression is that the best fit
line passes through the point represented by the mean X and mean Y
values.
They then regress ALST on TEX86 as shown in Figure S4, for which the
regression residuals have a standard error of 2.1 dC, and then use this
line to «forecast» temperature from past
values of TEX86 at various depths down the core (not tabulated anywhere, unfortunately).
nobody would suggest doing a
regression on that
line to arrive at an estimate of the true
value.
Or are you testing which of the
values (representing
regressions) in the population of
values is different from a «zero» that is actually the slope of the
regression line for the whole period?
A least - squares fit
regression line for the simulations (solid
line) and the observed seasonal cycle Δαs / ΔTs
value based on ISCCP and ERA40 reanalysis (dashed vertical
line) are also shown.
For example, the correlation between the variables in Figure 9 - 1 is 0.88, which means that the
regression line explains 100 × 0.882 = 77.4 percent of the variability in the temperature
values.
Linear
regressions are provided (green
lines) together with
value of the slope and goodness - of - fit (R2).
That
value is also in
line with F2xCO2 of 4.53 W / m2 estimated from a Gregory - plot
regression over the 35 years following an abrupt quadrupling of CO2.
With the effects of other covariates and the classification effects subsumed in the intercept of the equations, the vertical distance between the
regression lines represents the estimated mean difference at a given covariate
value on the abscissa.
Preliminary analyses using statistical analysis system (SAS Institute, Cary, NC) were carried out to detect any missing
values or outliers with large influences on the
regression lines.
Note:
Lines depict the simple
regression line for
values of child temperament 1 SD above and below the mean.