Linear Regression and Correlation. Fitted Regression Line. Equation of the Regression Line. Least squares regression line of Y on X. Regression Calculations. Plotting the regression line. Residuals. Using the fitted line, it is possible to obtain an estimate of the y coordinate.
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Least squares regression line of Y on X
Model Residuals: freely moving
Population mean Y value for a given X
Population SD of Y value for a given X
estimatesStatistical inference concerning
Using the test statistic:
Line “captures” most of the data variance. from zero?
What’s this? from zero?
It adjusts R to compensate for the fact
That adding even uncorrelated variables to
the regression improves R
STA example from zero?
is not a function of X
Y1 = X1 + X2 + X3 +...+ Xn
(metric DV) (non-metric IV’s)
Y1 + Y2 + ... + Yn = X1 + X2 + X3 +...+ Xn
(metric DV’s) (non-metric IV’s)
Reject the null hypothesis if test statistic is greater than critical F value with k-1
Numerator and N-k denominator degrees of freedom. If you reject the null,
At least one of the means in the groups are different
Individual ANOVAs not significant
Overall multivariate effect is signficant
MANOVA from zero?
So if you remove the amount the subjects intend to spend from the equation,
No significant difference between spending. Spending difference not a result
Of “impulse buys”, it seems.
Example: 8 channels of recorded EMG activity from zero?
Note how a single component explains series as a spatial vector) to a “position” in the abstract space that minimizes covariance.
almost all of the variance in the 8 EMGs
Next step would be to correlate
these components with some
other parameter in the experiment.
Largest PC series as a spatial vector) to a “position” in the abstract space that minimizes covariance.
Neural firing rates