# Linear regression Vs Logistic regression

I have a time series dataset. The,

X (Independent variable) is time and is denoted as 1,2,3,4,5,6..1000.etc Y (Dependent variable ) is a percentage scale as 99%, 98.7%, 96%, 91% ...etc. This is a continuous data set.

I have 1000 such data points. The first 700 data points used as training set and rest 300 is used for testing.

I tried to use simple linear regression but when predicting sometimes the prediction is more than 100%. And the case is even worse when I calculated the confidence interval and prediction interval.

So I tried to use logistic regression as there is a boundary ( from 0% to 100%). But logistic regression can take only binary data. I am confused on how to appropriately convert my existing time series data so that I can try how logistic regression on that.

You're correct that logistic regression is only for binary response data, which is not applicable here. What you may be wanting to do is simply apply the logit transform to the response data (i.e. the $Y$ values) and then use linear regression on the transformed data. Then apply the inverse logit transform to predictions to put them back on the original scale.
• There is also the variance stabilized arcsine square root transformations if $Y$ is a proportion. – Frank Harrell Mar 12 '16 at 16:37