Tagged Questions

82 views

Does more variables mean tighter confidence intervals?

Assume that the true (but unknown) relationship in a population between $Y$ and $X1, X2, X3, X4$ is $$Y=\beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 + \beta_4 X_4.$$ Further assume that I have a ...
110 views

Why do we estimate the mean response in Confidence interval but predict individual outcome in prediction?

I have tried to understand the differences. Just to be clear, I think I understand the two sources of variation in prediction comes from the variation in the distribution of the location of Y and ...
100 views

Calculating Prediction Interval

I have the following data located here. I am attempting to calculate the 95% confidence interval on the mean purity when the hydrocarbon percentage is 1.0. In R, I enter the following. ...
88 views

What can I do if the confidence intervals of the predicted mean are small but the predicted intervals are large

I am conducting a linear regression: $Y=\alpha+\beta\times X+\epsilon$, $\epsilon\sim N(0,\sigma^2)$. It turned out that the confidence interval for the predicted mean $Y$ was really small (figure 1), ...
66 views

Confidence or prediction limits for significant difference between forecast and observation?

My task is to to forecast business data without advertising and compare the real observations (with advertising effect) to the forecasted values in order to measure the effect of advertising. I am ...
168 views

How to get prediction intervals at mean & at max of covariate values in R

I'm still working on R problems from a book, and using my spending data. Part 1: I need to predict the amount that a male with average data for status, income and verbal would spend along a 95% CI. ...
249 views

Calculating prediction intervals when using cross validation

Are standard deviation estimates calculated via: $s_N = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2}.$ (http://en.wikipedia.org/wiki/Standard_deviation#Sample_standard_deviation) for ...
1k views

Computing prediction intervals for logistic regression

I would like to understand how to generate prediction intervals for logistic regression estimates. I was advised to follow the procedures in Collett's Modelling Binary Data, 2nd Ed p.98-99. After ...
255 views

Why doesn't the exponential smoothing forecast package in R provide confidence intervals for the fitted values?

The upper and lower prediction intervals for the forecast periods are provided by the forecast() function. However, neither prediction or confidence intervals seem to be available for the fitted ...
For a prediction interval in linear regression you still use $\hat{E}[Y|x] = \hat{\beta_0}+\hat{\beta}_{1}x$ to generate the interval. You also use this to generate a confidence interval of ...