Terms and Linear Reggresion

Question 1

Response / dependent variable

Answer 1

The variable of interest, dependent on other explanatory variables.

Question 2

Explanatory / independent variables.

Answer 2

Other variables that are used to explain the behaviour of the response variable.

Question 3

Factor

Answer 3

Is a discrete explanatory variable

Question 4

What are covariates

Answer 4

Continuous explanatory variables

Question 5

Continuous variable

Answer 5

Things that can be counted infinite number of times such as age, measurement, temperature ect (although age can be converted to discrete if you seclude it to years).

Question 6

Discrete variable

Answer 6

A variable you can count a finite amount of time. Counting the change in your pocket.

Question 7

When a researcher manipulates the explanatory variables (treatments) while holding the other variables constant and notice the consequences of the response variable.

Answer 7

Designed experiments

Cause and effect relationships can be concluded

Question 8

Researchers observe the differences in explanatory variables and see if these are related to differences in the response variable.

Answer 8

Observational studies

Cannot be certain on cause and effect relationships.

Question 9

Confounding factors

Answer 9

Factors that affect both the dependent and independent variables.

Question 10

Correlation coefficient

r=

Answer 10

-1 to 1 score of linear relationships
0 = no linear relationship
1 = high positive relationship
-1 = high negative relationship

Question 11

Beta 0 =

Answer 11

The intercept

Question 12

Beta 1 =

Answer 12

The slope (change in Y when x is increased by 1 unit).

Question 13

Residual

Answer 13

Vertical distance between a data point and the regression line. Often named errors.

Question 14

Response Variable/s:

Answer 14

response variable is also referred to as a dependent variable.

Question 15

Explanatory Variable/s:

Answer 15

These are variables that are used to explain the effect

that we see in the response variable.

Question 16

independent variables.

Answer 16

physical elements that
reflect the design; for example, plots, animals, pens, test tubes or plants. There will also be the treatment elements. These could be diets, varieties, pasture types
etc.

Question 17

Predictor Variable (x)

Answer 17

Independent or explanatory variables which seek to predict or ‘explain’ the response variable.

Question 18

Dependent Variable (Y ):

Answer 18

Response variable of interest to investigators that is (hopefully) dependent on the explanatory variable/s. This is always a random variable.

Question 19

dependent variable goes on the __ axis

Answer 19

Y

Question 20

independent variable always sits on the __ axis

Answer 20

X

Question 21

calculate rXY (rcmdr)

Answer 21

Statistics / Summaries / Correlation Matrix , then press “OK”, then select the variables whose correlation coefficient(s) you want to find

Question 22

Yi = β0 + β1xi + εi

Answer 22

simple linear reggression model.

Question 23

The random error term is assumed to:

Answer 23

follow a normal distribution,
have a mean of zero: E(εi) = 0,
have a constant variance: Var(εi) =σ2
be uncorrelated with the other error terms.

Question 24

a simple linear regression

model (Rcmdr)

Answer 24

Statistics / Fit Models / Linear

Regression

Question 25

correlation coefficient is between;

Answer 25

-1 and +1

Question 26

B1 = slope, the change in;

Answer 26

y when x is increased by 1.

Question 27

smaller sum of squares indicates;

Answer 27

better fitting line.

Question 28

The coefficient of determination

Answer 28

a measure of the variability in the response variable that is explained by the predictor variable. r2

Question 29

hypothesis testing for B1 =

Answer 29

H0: B1 = 0
H1: B1 not=0

Question 30

The coefficient of determination (R2)

Answer 30

a measure of the variability in the response variable that is explained by the predictor variable x2

Question 31

curvilinear

Answer 31

contained by or consisting of a curved line or lines.

Question 32

when to use a polynomial reggression model?

Answer 32

You would use a polynomial regression model if the aim was to define the relationship between two continuous variables, as you would do for simple linear regression.
The difference is that the relationship between the response variable and the predictor variable is suspected to be curved, rather than being linear.

Question 33

process of fitting a linear reggression model 5 steps:

Answer 33

1. Graph the data to determine the type of relationship
2. Fit an appropriate model
3. Test the assumptions
4. Check the fit of the model
5. Draw conclusions

Question 34

polynomial function: parabola

Answer 34

a polynomial function where the highest power is a squared (2) term (for the parabola)

Question 35

polynomial function: cubic

Answer 35

a polynomial function where the highest power is a cubed (3) term (for the cubic)

Question 36

B0 (beta zero) =

Answer 36

Value of y when x is equal to 0.

Question 37

Residual is

Answer 37

Calculation of distance between line of best fit and points.

Question 38

A smaller sim of squares indicates what?

Answer 38

A better fitting line.

Question 39

Best graph to use for 2 continuous variables?

Answer 39

Scatterplot

Question 40

Simple linear regression model analysis has 3 major purposes.

Answer 40

1. To describe the linear relationship between X and Y
2. To determine how much of the variation in Y can be explained by the linear relationship.
3. To predict new values of Y from given values of X.

Question 41

Coefficient of determination

Answer 41

A statistical measurement that examines how differences in one variable can be explained by differences in another when predicting the outcome of an active vent.