1 vote
3k views

### What is the Formula for Prediction Interval in Multivariate Case? [duplicate]

I am using linear model to do prediction, and I would like to calculate my prediction's prediction interval, which, when there is only one predictor, is However, my model has three predictors. What ...
• 123
1 vote
439 views

### Reproduce a confidence interval of linear regression in Excel [duplicate]

After a series of tests and exploratory analysis, I have design a linear model in R, the model is the following: ...
• 255
63 views

### confidence intervals for predicted values in linear regression [duplicate]

I have made this linear regression model: mtcars_lm <- lm(mpg ~ drat + hp, mtcars) Using the effects package, I can predict values of ...
• 14.5k
1 vote
35 views

### Calculating error bars for Excel Linear Regression [duplicate]

I've ben sent a forecast of sales from a consultancy. It uses Excel's LINEST function, taking 4 factors that seem to have affected sales in the past, and used them to make a prediction. How do I go ...
1 vote
29 views

### Confidence Intervals for Outputs of Regression? [duplicate]

Suppose I have some reasonably sized dataset and I do linear regression on it, so now I have a model, say $\hat{y}=Ax+b$, where $y$ is real (or perhaps a vector, but let's say real for now), $x$ (my ...
• 355
215k views

### Difference between confidence intervals and prediction intervals

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 $E[Y|x_0]$....
• 1,525
10k views

### Linear regression prediction interval

If the best linear approximation (using least squares) of my data points is the line $y=mx+b$, how can I calculate the approximation error? If I compute standard deviation of differences between ...
• 241
9k views

### Gaussian process prediction interval

How can the prediction interval of a Gaussian process be evaluated? I don't know how to estimate this interval though I can find a 95 % confidence interval for the mean line.
• 2,204
23k views

### Calculation of variance of prediction

Could anybody show me how @Rob Hyndman calculates the variance of $\hat{y}$ in the following link Obtaining a formula for prediction limits in a linear model : EDIT: Basically I don't understand how ...
• 355
2k views

### Derivation of confidence and prediction intervals of predictions for probit and logit (and GLMs in general)

The derivation of the prediction interval for the linear model is quite simple: Obtaining a formula for prediction limits in a linear model . How to derive the confidence and prediction intervals for ...
3k views

### How to calculate the specific Standard Error relevant for a specific point estimate within a linear regression?

My objective is to actually get to the Standard Error for every point estimate of a linear regression. I originally thought that the Standard Error of a linear regression model was constant. And, ...
• 7,812
8k views

### Propagation of polynomial coefficient errors in fit

I fit a cubic function (in mathematica) $$y(x) = a + b x + c x^2 + d x^3$$ to my data and obtained a function. I have the error in each coefficient ($\sigma_a$, $\sigma_b$, $\sigma_c$, \$\...
• 51
2k views

### Can we make probabilistic statements with prediction intervals?

I've read through the many excellent discussions on the site regarding interpretation of confidence intervals and prediction intervals, but one concept is still a bit puzzling: Consider the OLS ...
• 641
8k views

### How to do prediction from a linear regression?

I am not very good in statistics (ok, I'm really bad), I guess this is a very simple question but I dont understand much of the literature. I have a dataset that is arranged in 2 columns (...
• 115
1 vote