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forest biometrics exam 2 Questions and
Answers (Expert Solutions)
Q: regression analysis, 🗹🗹: To study the relationship between X and Y we perform
Q: Regression:, 🗹🗹: the statistical or mathematical relationship between the
independent variable (X) and a dependent variable (Y) while considering certain
constants or parameters
Q: dependent varible, 🗹🗹: The quantity being estimated through regression is called
the
Q: independent variable, 🗹🗹: is measured in order to predict the dependent variable
Q: scatter diagrams, 🗹🗹: One way to examine the x and y relationship is through
Q: Once the X,Y points are plotted, the diagram can be analyzed to see if a ------ forms.,
🗹🗹: pattern
Q: The simplest relationship is called a ---- ---- ---- which is also called a straight line
relationship, 🗹🗹: simple linear regression
Q: 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 --, 🗹🗹: X,
Y ..... Yi, Xi
Q: linear model equation, 🗹🗹: Y^=A + BX
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Q: prediction equation, 🗹🗹: an equation suggested by the points of a scatter plot
that is used to predict other points
Q: is a way for us to get the estimates needed, in other words values for a and b, 🗹🗹:
least squares
Q: So what do we need for least squares?, 🗹🗹: 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
Q: Least Squares allows us to get the best, 🗹🗹: unbiased estimates
Q: So for every observed Yi there is a predicted value of --, equal to (a + bXi ) which
corresponds to a location on the regression line, 🗹🗹: Y^i
Q: (yi-y^i), 🗹🗹: is the deviation of the observed Y from the predicted Y^
Q: sum(Yi-Y^)2, 🗹🗹: The sum of squares of all the deviations form the fitted line :
Q: Since we know Y^ = a + bX, we can substitute for Y^ in the formula to get:, 🗹🗹:
sum(Yi - a - bXi ) 2
Q: 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,
🗹🗹: prediction equation Y^ = a + bX
Q: 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), 🗹🗹: regression assumptions:
forest biometrics exam 2 Questions and
Answers (Expert Solutions)
Q: regression analysis, 🗹🗹: To study the relationship between X and Y we perform
Q: Regression:, 🗹🗹: the statistical or mathematical relationship between the
independent variable (X) and a dependent variable (Y) while considering certain
constants or parameters
Q: dependent varible, 🗹🗹: The quantity being estimated through regression is called
the
Q: independent variable, 🗹🗹: is measured in order to predict the dependent variable
Q: scatter diagrams, 🗹🗹: One way to examine the x and y relationship is through
Q: Once the X,Y points are plotted, the diagram can be analyzed to see if a ------ forms.,
🗹🗹: pattern
Q: The simplest relationship is called a ---- ---- ---- which is also called a straight line
relationship, 🗹🗹: simple linear regression
Q: 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 --, 🗹🗹: X,
Y ..... Yi, Xi
Q: linear model equation, 🗹🗹: Y^=A + BX
, Page | 2
Q: prediction equation, 🗹🗹: an equation suggested by the points of a scatter plot
that is used to predict other points
Q: is a way for us to get the estimates needed, in other words values for a and b, 🗹🗹:
least squares
Q: So what do we need for least squares?, 🗹🗹: 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
Q: Least Squares allows us to get the best, 🗹🗹: unbiased estimates
Q: So for every observed Yi there is a predicted value of --, equal to (a + bXi ) which
corresponds to a location on the regression line, 🗹🗹: Y^i
Q: (yi-y^i), 🗹🗹: is the deviation of the observed Y from the predicted Y^
Q: sum(Yi-Y^)2, 🗹🗹: The sum of squares of all the deviations form the fitted line :
Q: Since we know Y^ = a + bX, we can substitute for Y^ in the formula to get:, 🗹🗹:
sum(Yi - a - bXi ) 2
Q: 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,
🗹🗹: prediction equation Y^ = a + bX
Q: 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), 🗹🗹: regression assumptions:
