8.9.1 Consider the data in the following table. ... ... Plot yield (Y ) against weight (W ). Suppose we think that the line Y = W + 0.6 describes these data. Plot the line on your graph of yield against weight. Find and plot the residuals.
Get solution
8.9.2 Consider the data in the following table. ... ... Plot height (H) against weight (W). Suppose we think that the line H = 8W + 5 describes the data. Plot the line on your graph of height against weight. Find and plot the residuals.
Get solution
8.9.3 Consider the data in the following table. ... ... Find SSE for the model used in Exercise 1
Get solution
8.9.4 Consider the data in the following table. ... ... Find SSE for the model used in Exercise 2
Get solution
8.9.5 Consider the data in the following table. ... ... Find the null model that best fits Y as a function of W and find SST.
Get solution
8.9.6 Consider the data in the following table. ... ... Find the null model that best fits H as a function of W and find SST.
Get solution
8.9.7 Consider the data in the following table. ... ... Find ...for the model in Exercise 1.
Get solution
8.9.8 Consider the data in the following table. ... ... Find ...for the model in Exercise 2.
Get solution
8.9.9
Consider the data in the following table. ... ...
Compute the best fitting line for yield as a function of weight. Graph
the line.
Get solution
8.9.10
Consider the data in the following table. ... ...
Compute the best fitting line for height as a function of weight. Graph
the line.
Get solution
8.9.11 Consider the data in the following table. ... ... Find SSE for the line in Exercise 9, find ..., and compare with the model in Exercise 1.
Get solution
8.9.12 Consider the data in the following table. ... ... Find SSE for the line in Exercise 10, find ..., and compare with the model in Exercise 2.
Get solution
8.9.13
Consider the data in the following table. ... ... Find
the correlation between weight and yield. Check that its square is
equal to the value of ...found in Exercise 11.
Get solution
8.9.14
Consider the data in the following table. ... ... Find
the correlation between weight and height. Check that its square is
equal to the value of ...found in Exercise 12.
Get solution
8.9.15 Linear
regression has important connections with other techniques in
statistics, such as testing whether two populations differ. In the
following data set, the independent variable takes on only two values.
Find the best fitting line and ...,
and then test whether the two sets of points differ in their mean
distribution using the techniques in Section 8.6. Assume that the data
are normally distributed with known variance of 25. In each case, graph
the regression line and the data. ... Find the best fitting line and ...for replicate 1 and then test whether the diet has a significant effect.
Get solution
8.9.16 Linear
regression has important connections with other techniques in
statistics, such as testing whether two populations differ. In the
following data set, the independent variable takes on only two values.
Find the best fitting line and ...,
and then test whether the two sets of points differ in their mean
distribution using the techniques in Section 8.6. Assume that the data
are normally distributed with known variance of 25. In each case, graph
the regression line and the data. ... Find the best fitting line and ...for replicate 2 and then test whether the diet has a significant effect. Compare with the previous problem.
Get solution
8.9.18 Best fit regression lines have many nice properties. Show
that the best linear fit from Theorem 8.6 passes through the center of
the data in the sense that the sum of the residuals is 0.
Get solution
8.9.18 Best fit regression lines have many nice properties. Show
that the best linear fit from Theorem 8.6 passes through the center of
the data in the sense that the sum of the residuals is 0.
Get solution
8.9.19 Best fit regression lines have many nice properties. Consider models of the form Y = b. Show that the sum of the squares of the residuals is minimized when ...the sample mean of the ... .
Get solution
8.9.20 Best fit regression lines have many nice properties. Consider models of the form Y =aX. Find the slope that minimizes the sum of the squares of the residuals.
Get solution
8.9.21 Consider the following measurements. ... Find the best linear fit. Plot the line and find ...How good is the model?
Get solution
8.9.22
Consider the following measurements. ... Use the principle of
least squares to write the expression you would use to fit a curve of
the form .... One easy way to solve this is to think of a new measurement ...and find the linear regression of Y on Z . Plot the linear regression of Y against Z and the curved regression of Y against .... Which model does better?
Get solution
8.9.23 Consider the following measurements. ... Find the dimensions of the slope ...
Get solution
8.9.24
Consider the following measurements. ... Find the dimensions
of the intercept ...and check that all the parts of the equation match.
Get solution
8.9.25 Consider the following data describing change in a bacterial population. ... Find .... Graph the data and the line.
Get solution
8.9.26
Consider the following data describing change in a bacterial
population. ... Find the best fitting line, and compare with a
mathematically idealized model. Which makes more sense ?
Get solution
8.9.27
Consider the following data on the growth of two bacterial
populations. ... Find the best fitting line for population 1 as a
function of time and ....
Get solution
8.9.28
Consider the following data on the growth of two bacterial
populations. ... Find the best fitting line for population 2 as a
function of time and compute ...
Get solution
8.9.29
Consider the following data on the growth of two bacterial
populations. ... Find the best fitting line for the logarithm of
population 1 as a function of time and compute .... Is this a better fit?
Get solution
8.9.30
Consider the following data on the growth of two bacterial
populations. ... Find the best fitting line for the
logarithm of population 2 as a function of time and compute .... Is this a better fit?
Get solution
8.9.31
Consider
the following data which include one outlying point. Find the best
fitting line with and without that point. How much difference does that
point make? The idea of removing one point and testing how much the fit
changes is an important tool in regression, and is sometimes called the
leverage of that point. ... Find the best fitting line and ...for replicate 1 with and without the fourth point. Graph the two regression lines and the data.
Get solution
8.9.32
Consider
the following data which include one outlying point. Find the best
fitting line with and without that point. How much difference does that
point make? The idea of removing one point and testing how much the fit
changes is an important tool in regression, and is sometimes called the
leverage of that point. ... Find the best fitting line and ...for
replicate 2 with and without the last point. Graph the two regression
lines and the data. Why do you think the outlier affects this regression
line more?
Get solution
8.9.33 The following table gives the winning Olympic times for men and women in the 400 m race. ...
a. Use your computer to find the best linear regression for men and for women.
b. Plot the residuals for each. Does the linear model fit well?
c. Predict the times in the 2000 Olympics for women and men. How well did it actually work?
d. Predict when women will outrun men. Do you believe this?
Get solution
