An ANCOVA revealed that the fitted
linear regression lines have a significantly different slope (rostral CCF 1.872 ± 0.5159, caudal CCF 4.532 ± 1.148 [p = 0.03668], see Figure 6), indicating that in CKCS, crowding of cerebellum in the caudal part of the CCF is more sensitive to changes in the relative volume of the cerebellum than in the rostral part of the CCF.
Fitted
linear regression lines are also displayed.
To quantify these topographic relations we fitted
linear regression lines (solid) to each of the three datasets.
Graph 4 shows descriptive statistics of indicators 1) and 2) against total travel expenses for each MP and includes fitted
linear regression lines.
Shaded region is the 95 % confidence band of
the linear regression line.
The linear regression line for the % of stocks oversold and average p / l % seem to be diverting.
The last thing I expected was an up sloping
linear regression line.
A linear regression line through a change of temperature with time, or a sinusoidal fit to the seasonal cycle for instance.
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.
Note that the number of confirmed erupting volcanoes has leveled off between 50 and 70 per year through the past four decades, and
a linear regression line through the data indicates that volcanism has been virtually constant.
Having said that
the linear regression line might well give an overestimate if non-linear effects are accelerating the melt rate, but even if not, there is no cause for complacency.
Using
the linear regression line allows us to predict an annual anomaly of 1.08 °C.
Not exact matches
The most familiar example of this might be
linear regression, which finds a
line that approximates a distribution of data points.
Straight
lines represent the
linear regression applied to each curve starting with day 4 postgermination.
Solid (− / −) and dashed (+ / +)
lines show the
linear regression correlation between age and absolute number of cells.
To complete the task cards students will use knowledge of
linear regressions (
line of best fit, least squares
regression), correlation coefficients, and calculating residuals and their meaning.
It's called a
linear regression because you literally draw a straight
line through a scatterplot of a manager's returns and the benchmark.
The goal of the
linear regression is to get a
line that best fits the data.
I used Excel to determine
regression equations (i.e., straight -
line,
linear curve fits).
The green
line is a
linear regression of the data.
I used Excel's plotting function to calculate
regression equations (i.e.,
linear, straight -
line curve fits) of the dividend amount at Year 10 and at Year 20 versus the percentage earnings yield 100E10 / P.
The straight
lines show the best
linear - fit against time estimated through
linear regression.
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.
The «basis» for
linear regression is that if the noise (deviation from the model) follows the normal distribution, then
linear regression is the maximum - likelihood solution for a straight -
line fit.
But a trend
line produced from some statistical procedure, such as
linear regression, is meaningful only if a trend actually exists.
«After many requests, I finally added trend -
lines (
linear least - squares
regression) to the graph generator.
The
lines show best
linear regression with correlation r.
He's performing a
linear least - squares
regression, which only knows the two end - points and draws the best - fit straight
line between the two.
No
linear relationship is assumed or implied, so models such as 7 receive a large weight because they are consistent with the data, although they lie far from any
regression line.
All it actually means is the
linear regression model doesn't fit the data perfectly, but of course not, that's to be expected given temperature data doesn't follow a perfect
line.
However, although its simple
linear regression analysis facilities (including polynomials) provides automatically the option for plotting the fit with CIs for the fitted
line / curve and for future observations from the same population, I am unsure about these intervals for autocorrelated data — typically time series.
There appears to be an overall decline, as indicated by the blue
line, which is a
linear regression fit to estimate the overall trend.
A
linear regression trend
line with normal iid error gets to the heart of what Mandelbrot was questioning.
A running mean merely smooths, it doesn't give a trend
line, unlike
linear regression, meaning least - squares fit of a straight
line.
If the data are adequate and the true
line is a straight
line, then
linear regression via least squares will produce an unbiased and normally distributed estimate of the slope and intercept.
procedures that... first infer a
linear relation (
regression line) between ECS and variables... from models and then use that
linear relation to constrain ECS given observations... can be strongly influenced by «bad» models that are not consistent with the data but exert large leverage on the inferred slope of the
regression line.
We'll also compute the standard deviation of the residuals from our
linear regression so we can add two
lines to the graph, one of which is two standard deviations above our forecast, the other two standard deviations below, in order to delineate the range in which we would expect most of the future data to be.
First, the fit of the dark - blue deseasonalized NOAA data to the underlying
linear -
regression trend
line (light blue) is very much closer than it is even to the IPCC's least projection on scenario A2.