Forest
Forest Biometrics Best Set with Correct
Answers Exam 2025
regression analysis - Correct Ans-To study the relationship between X and Y we
perform
Regression: - Correct Ans-the statistical or mathematical relationship between the
independent variable (X) and a dependent variable (Y) while considering certain
constants or parameters
dependent varible - Correct Ans-The quantity being estimated through regression is
called the
independent variable - Correct Ans-is measured in order to predict the dependent
variable
scatter diagrams - Correct Ans-One way to examine the x and y relationship is through
Once the X,Y points are plotted, the diagram can be analyzed to see if a ------ forms. -
Correct Ans-pattern
The simplest relationship is called a ---- ---- ---- which is also called a straight line
relationship - Correct Ans-simple linear regression
There is an assumption, for each -- value a distribution for the -- values will occur with
each observation of i, at observation -- there will be an observation at -- - Correct Ans-X,
Y ..... Yi, Xi
linear model equation - Correct Ans-Y^=A + BX
prediction equation - Correct Ans-an equation suggested by the points of a scatter plot
that is used to predict other points
is a way for us to get the estimates needed, in other words values for a and b - Correct
Ans-least squares
So what do we need for least squares? - Correct Ans-1. Estimates of A and B by using
a and b
2. We use the estimates of a and b in the prediction equation Y^= a + bX
3. Get estimates of a and b variances 4. Test hypothesis 5. Set confidence intervals 6.
And on occasion, estimate Y for a given value of X
Forest
, Forest
Least Squares allows us to get the best - Correct Ans-unbiased estimates
So for every observed Yi there is a predicted value of --, equal to (a + bXi ) which
corresponds to a location on the regression line - Correct Ans-Y^i
(yi-y^i) - Correct Ans-is the deviation of the observed Y from the predicted Y^
sum(Yi-Y^)2 - Correct Ans-The sum of squares of all the deviations form the fitted line :
Since we know Y^ = a + bX, we can substitute for Y^ in the formula to get: - Correct
Ans-sum(Yi - a - bXi ) 2
When a and b have been found their numerical values (using the previous two formulas
and the data) for the two estimators a and b can be substituted into the - Correct Ans-
prediction equation Y^ = a + bX
1. A and B are unknown parameters or also referred to as constants 2. X's are known
values (measured values with no associated errors) and are selected by the user 3. For
each value of X, the Yi ~ N(µ,σ 2 ) and independent 4. The variance of Y with a given X
is the same for all X (homoscedasticity) - Correct Ans-regression assumptions:
Steps of Linear Regression pt 1 - Correct Ans-1. Identify variables that can contribute
and set goals 2. Lit review, have others already used similar models? 3. Use other fields
of study such as biology, natural resource management, economics, etc. to look at their
logic with relationships and principles/theory of those relationships. 4. Identify:
dependent and independent variables 5. What is the shape of the relationship? (Scatter
Diagram) 6. Design a scheme for data collection and sampling 7. Collect Data 8. Plot
raw data
steps of linear regression pt 2 - Correct Ans-9. When looking at the plot, how does it
compare to others (based on lit reviews what are your expectations?) 10. Select the
regression model 11. Apply transformations if needed 12. Estimate parameters 13. For
different levels of X, use regression to predict Y 14. Plot the Y predicted values on the
data and draw the curve 15. Evaluate your findings
We need a more precise way to see how well the model serves the data and shows
strength of the relationships. We can do this with a method called - Correct Ans-
Partitioning Sum of Squares (PSSR)
isolates the sum of squares (variation) among sample Y's (comparing the variation of X
to the variation of Y). Part of the variation can be attributed to the relationship between
X and Y. - Correct Ans-PSSR
random error - Correct Ans-is another sources of variation (here error is a statistical
term for deviation)
Forest
Forest Biometrics Best Set with Correct
Answers Exam 2025
regression analysis - Correct Ans-To study the relationship between X and Y we
perform
Regression: - Correct Ans-the statistical or mathematical relationship between the
independent variable (X) and a dependent variable (Y) while considering certain
constants or parameters
dependent varible - Correct Ans-The quantity being estimated through regression is
called the
independent variable - Correct Ans-is measured in order to predict the dependent
variable
scatter diagrams - Correct Ans-One way to examine the x and y relationship is through
Once the X,Y points are plotted, the diagram can be analyzed to see if a ------ forms. -
Correct Ans-pattern
The simplest relationship is called a ---- ---- ---- which is also called a straight line
relationship - Correct Ans-simple linear regression
There is an assumption, for each -- value a distribution for the -- values will occur with
each observation of i, at observation -- there will be an observation at -- - Correct Ans-X,
Y ..... Yi, Xi
linear model equation - Correct Ans-Y^=A + BX
prediction equation - Correct Ans-an equation suggested by the points of a scatter plot
that is used to predict other points
is a way for us to get the estimates needed, in other words values for a and b - Correct
Ans-least squares
So what do we need for least squares? - Correct Ans-1. Estimates of A and B by using
a and b
2. We use the estimates of a and b in the prediction equation Y^= a + bX
3. Get estimates of a and b variances 4. Test hypothesis 5. Set confidence intervals 6.
And on occasion, estimate Y for a given value of X
Forest
, Forest
Least Squares allows us to get the best - Correct Ans-unbiased estimates
So for every observed Yi there is a predicted value of --, equal to (a + bXi ) which
corresponds to a location on the regression line - Correct Ans-Y^i
(yi-y^i) - Correct Ans-is the deviation of the observed Y from the predicted Y^
sum(Yi-Y^)2 - Correct Ans-The sum of squares of all the deviations form the fitted line :
Since we know Y^ = a + bX, we can substitute for Y^ in the formula to get: - Correct
Ans-sum(Yi - a - bXi ) 2
When a and b have been found their numerical values (using the previous two formulas
and the data) for the two estimators a and b can be substituted into the - Correct Ans-
prediction equation Y^ = a + bX
1. A and B are unknown parameters or also referred to as constants 2. X's are known
values (measured values with no associated errors) and are selected by the user 3. For
each value of X, the Yi ~ N(µ,σ 2 ) and independent 4. The variance of Y with a given X
is the same for all X (homoscedasticity) - Correct Ans-regression assumptions:
Steps of Linear Regression pt 1 - Correct Ans-1. Identify variables that can contribute
and set goals 2. Lit review, have others already used similar models? 3. Use other fields
of study such as biology, natural resource management, economics, etc. to look at their
logic with relationships and principles/theory of those relationships. 4. Identify:
dependent and independent variables 5. What is the shape of the relationship? (Scatter
Diagram) 6. Design a scheme for data collection and sampling 7. Collect Data 8. Plot
raw data
steps of linear regression pt 2 - Correct Ans-9. When looking at the plot, how does it
compare to others (based on lit reviews what are your expectations?) 10. Select the
regression model 11. Apply transformations if needed 12. Estimate parameters 13. For
different levels of X, use regression to predict Y 14. Plot the Y predicted values on the
data and draw the curve 15. Evaluate your findings
We need a more precise way to see how well the model serves the data and shows
strength of the relationships. We can do this with a method called - Correct Ans-
Partitioning Sum of Squares (PSSR)
isolates the sum of squares (variation) among sample Y's (comparing the variation of X
to the variation of Y). Part of the variation can be attributed to the relationship between
X and Y. - Correct Ans-PSSR
random error - Correct Ans-is another sources of variation (here error is a statistical
term for deviation)
Forest
