Lesson 3 - Estimation of Tree Volume

Question 1

What is linear regression

Answer 1

linear regression is used to relate on dependent variable (y) to independant variables (x’s)

Question 2

What is simple linear regression and what is it used to find

Answer 2

only one independent variable, used to find estimates of the slope and intercept from simple data
once obtained we can:
- determine how well the regression line fits the sample data (goodness of fit)
- calculate confidence intervals for the true slope and intercept (population)
- calculate confidence intervals for the mean predicted y value (y value on the regression line)
- test whether the regression line is signifigant

Question 3

What assumptions must be met for simple linear regression

Answer 3

1. the relationship between x and y is linear
2. the variance of the y values must be the same for every x value
3. each observation (x,y) must be independent of all other observations
4. the y value must be normally distributed for each x value
5. the x value must be measured without error
6. the y values are selected randomly for each x value

Question 4

explain SSX and SPXY

Answer 4

SSX = sum of squares of x
= sum of x squared - (sum of x) squared/n

SSXY = sum of product xy
= sum of x*y - (sum of x)(sum of y)/n

Question 5

What is b0 and b1, and how is SSX and SPXY related?

Answer 5

b0 and b1 are coefficients of the regression line

b1 is the slope
= SPXY/SSX

b0 is the y intercept
= mean of y - b1 * mean of x

finding these values will result in minimizing the sum of squared difference

Question 6

What is goodness of fit and how can we describe it

Answer 6

How well the line actually explains (fits) the data

can be explained through coefficient of determination and standard error of the estimate

Question 7

explain coefficient of determination

Answer 7

r squared
the amount of variation of the y observations accounted for by the regression, value will always be between 0 and 1
higher the value, higher the proportion of variation in y is accounted by the regression

Question 8

What is standard error

Answer 8

gives us an indication of how far the observations are spread around the regression line
68% of the sample observations will be within one standard error, 95% will be within two standard errors of the regression line

Question 9

what are confidence intervals

Answer 9

how we expect the population to behave

- how likely it is that if we took another sample set, we would obtain similar estimates of the slop and intercept

Question 10

What is the standard deviation

Answer 10

how much the estimates would be expected to vary for different sample sets
- can also be calculated for the mean predicted value of y for a given value of x