QMB 3250 Exam 2 (Module 10-16)
Fitted Line
Think of these estimates as the true values of Bo and B1.
Equation : Yhat= bo+b1x
Regression model
In reality, the meaning of the Ys at the X that don't line up with the value of Y, so the error term is
added to account for this. The E are unknown, but we study the e=residuals = Y-Yhat to
understand them.
Y=Bo+B1X+E
Previous
Play
Next
Rewind 10 seconds
Move forward 10 seconds
Unmute
0:02
/
0:15
Full screen
Brainpower
Read More
What would be the point estimate for B1?
b1
If we were to take another sample and collect other values of x and y, would you get the same
values of b0 and b1?
no, samples would vary
The spread around the line is measured by the...
residual standard deviation
We measure spread of the x values by using the...
, standard deviation of the x's
The smaller the standard error, the ...
easier it is to estimate. the smaller the se, the smaller the SE(b1) will be.
The larger the standard deviation (Sx), the...
easier it is to determine the slope, and the smaller the SE(b1) will be.
The larger the sample size, the...
easier will be to determine the slope, and the smaller the SE(b1) will be.
The standard error of the regression line - SE(b1) means...
the estimate of how much the slope of the regression lines vary from sample to sample.
Regression slope t test
Quantitative data
Hypothesis: Ho=0, Ha: not equal to 0
Sampling distribution: df=n-2
Regression slope t test assumptions:
1. linearity (both x and y have to be quantitative)
2. Independence assumption (randomization condition)
3. equal variance assumption (equal spread condition)
4. normal population assumption (errors have a normal distribution or very close. *This is more
important with smaller sample sizes)
Estimate the average y for a set x properties (confidence interval):
1. will be less than the prediction interval for an individual value of x.
2. the intervals are wider for values further away from the mean of x.
3. larger sample sizes will result in narrower intervals.
4. data with more spread around the line will result in wider intervals.
When using JMP, you look at the Mean Price 95% interval
Estimate an individual item at y for a set x (prediction interval) properties:
1. the standard error includes an extra term that estimates the spread around the line.
2. the prediction and triple is wider than a confidence interval for the same value of x.
Fitted Line
Think of these estimates as the true values of Bo and B1.
Equation : Yhat= bo+b1x
Regression model
In reality, the meaning of the Ys at the X that don't line up with the value of Y, so the error term is
added to account for this. The E are unknown, but we study the e=residuals = Y-Yhat to
understand them.
Y=Bo+B1X+E
Previous
Play
Next
Rewind 10 seconds
Move forward 10 seconds
Unmute
0:02
/
0:15
Full screen
Brainpower
Read More
What would be the point estimate for B1?
b1
If we were to take another sample and collect other values of x and y, would you get the same
values of b0 and b1?
no, samples would vary
The spread around the line is measured by the...
residual standard deviation
We measure spread of the x values by using the...
, standard deviation of the x's
The smaller the standard error, the ...
easier it is to estimate. the smaller the se, the smaller the SE(b1) will be.
The larger the standard deviation (Sx), the...
easier it is to determine the slope, and the smaller the SE(b1) will be.
The larger the sample size, the...
easier will be to determine the slope, and the smaller the SE(b1) will be.
The standard error of the regression line - SE(b1) means...
the estimate of how much the slope of the regression lines vary from sample to sample.
Regression slope t test
Quantitative data
Hypothesis: Ho=0, Ha: not equal to 0
Sampling distribution: df=n-2
Regression slope t test assumptions:
1. linearity (both x and y have to be quantitative)
2. Independence assumption (randomization condition)
3. equal variance assumption (equal spread condition)
4. normal population assumption (errors have a normal distribution or very close. *This is more
important with smaller sample sizes)
Estimate the average y for a set x properties (confidence interval):
1. will be less than the prediction interval for an individual value of x.
2. the intervals are wider for values further away from the mean of x.
3. larger sample sizes will result in narrower intervals.
4. data with more spread around the line will result in wider intervals.
When using JMP, you look at the Mean Price 95% interval
Estimate an individual item at y for a set x (prediction interval) properties:
1. the standard error includes an extra term that estimates the spread around the line.
2. the prediction and triple is wider than a confidence interval for the same value of x.
