An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics)
13th Edition
ISBN: 9781461471370
Author: Gareth James
Publisher: SPRINGER NATURE CUSTOMER SERVICE
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Chapter 3, Problem 6E
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Linear regression
- The least square line equation is
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In R, write a function that produces plots of statistical power versus sample size for simple linear regression. The function should be of the form LinRegPower(N,B,A,sd,nrep), where N is a vector/list of sample sizes, B is the true slope, A is the true intercept, sd is the true standard deviation of the residuals, and nrep is the number of simulation replicates. The function should conduct simulations and then produce a plot of statistical power versus the sample sizes in N for the hypothesis test of whether the slope is different than zero. B and A can be vectors/lists of equal length. In this case, the plot should have separate lines for each pair of A and B values (A[1] with B[1], A[2] with B[2], etc). The function should produce an informative error message if A and B are not the same length. It should also give an informative error message if N only has a single value. Demonstrate your function with some sample plots. Find some cases where power varies from close to zero to near…
"When conducting a binary regression with
a skewed predictor, it is often easiest to
assess the need for x and log(x) by including
them both in the model so that their relative
contributions can be assessed directly."
Show that indeed the log odds are a
function of x and log(x) for the gamma
distribution.
You perform experiments and determine the following values of heat capacity c at various temperatures T for a gas:
T (in deg C)
Cp (in J/Kg-K) 1256.00 1300.00 1398.00 1494.00 1587.00 1730.00
|-41.000 -16.000 10.000 47.000 95.000 113.000
1) Show the linear regression formulation to determine a model to predict Cp as a function of T, i.e., Cp = c + m T
2) Write a Matlab-code to computer the slope (m) and intersect (value of c).
3) For the above data-set, select all the correct choices for the least-squares regression line is.
Choices
Intercept, c=1292.81
O slope, m= 2.88
Oslope, m=3.46
Intercept, c= 1360.85
Chapter 3 Solutions
An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics)
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