02 Regression

Question 1

What gives a smaller Confidence Interval?

Random error (chance) can be controlled
by …

Coefficient of Determination
R2 measures the proportion of the variation in 𝑦 that is explained by the variation in 𝑥:

Answer 1

Larger sample size, Smaller Std deviation, Smaller Confidence level

statistical significance or by confidence interval

Explained SS/ TSS

Question 2

𝑡-Tests
Formula is slightly different for each:
* Single sample:
…
* Paired samples:
− tests the relationship between 2 linked samples, e.g., means obtained in
2 conditions by a single group of participants
* Independent samples:
…

Answer 2

− tests whether a sample mean is significantly different from a pre-existing value

− tests the relationship between 2 independent populations

Question 3

Selected Statistical Tests
Parametric Tests
* the family of 𝑡-tests: compares two sample means or tests a single sample mean * F-test: …
Non-parametric Tests
* Wilcoxon…
* Mann-Whitney-U test is used for—
* Kruskal-Wallis-Test for …
Tests of the Probability Distribution
* Kolmogorov-Smirnov and Chi-square test: used to determine whether…

Answer 3

compares the equivalence of variances of two samples

signed-rank test for 2 paired i.i.d samples
2 independent i.i.d samples
several i.i.d non-normally distributed samples

two underlying probability distributions differ, or whether an underlying probability distribution differs from a hypothesized distribution

Question 4

Adjusted R2
* It represents the proportion of variability of 𝑦 explained by 𝑋.
R2 is adjusted so that models with a different number of variables can be compared:

F-test
* Significant F indicates…
The t-test of each partial regression coefficient
* Significant t indicates that the …

Answer 4

1- RSS/(n-p-1) over TSS/(n-1)

a linear relationship between 𝑦 and at least one of the x’s: H:𝛽=𝛽=⋯=𝛽=0

variable in question influences the response
variable while controlling for other explanatory variables.

Backward/Fwd selection as subset selection