Tells you how accurate your estimate of the mean is likely to be. Calculated by the standard deviation of the observations divided by the square root of the sample size. You just studied 5 terms!

Standard error is the estimated standard deviation of an estimate. It measures the uncertainty associated with the estimate. Compared with the standard deviations of the underlying distribution, which are usually unknown, standard errors can be calculated from observed data.

Now, this is where everybody gets confused, the standard error is a type of standard deviation for the distribution of the means. Standard error measures the precision of the estimate of the sample mean.

The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.

The standard error tells you how accurate the mean of any given sample from that population is likely to be compared to the true population mean. When the standard error increases, i.e. the means are more spread out, it becomes more likely that any given mean is an inaccurate representation of the true population mean.

The margin of error (at 95% confidence) for our mean is (roughly) twice that value (+/- 0.26), telling us that the true mean is most likely between 2.94 and 3.46….Standard Error.

Standard errors are important because they reflect how much sampling fluctuation a statistic will show. The inferential statistics involved in the construction of confidence intervals and significance testing are based on standard errors. The standard error of a statistic depends on the sample size.

The standard error applies to any null hypothesis regarding the true value of the coefficient. Thus the distribution which has mean 0 and standard error 0.5 is the distribution of estimated coefficients under the null hypothesis that the true value of the coefficient is zero.

The standard deviation tells us how much variation we can expect in a population. We know from the empirical rule that 95% of values will fall within 2 standard deviations of the mean. 95% would fall within 2 standard errors and about 99.7% of the sample means will be within 3 standard errors of the population mean.

If you measure a sample from a wider population, then the average (or mean) of the sample will be an approximation of the population mean. The smaller the standard error, the less the spread and the more likely it is that any sample mean is close to the population mean. A small standard error is thus a Good Thing.

Approximately 95% of the observations should fall within plus/minus 2*standard error of the regression from the regression line, which is also a quick approximation of a 95% prediction interval.

A high standard error shows that sample means are widely spread around the population mean—your sample may not closely represent your population. A low standard error shows that sample means are closely distributed around the population mean—your sample is representative of your population.

The residual standard error is the standard deviation of the residuals – Smaller residual standard error means predictions are better • The R2 is the square of the correlation coefficient r – Larger R2 means the model is better – Can also be interpreted as “proportion of variation in the response variable accounted for …

Typical Prediction Error: Standard Error of Estimate That is, if the error distribution is normal, then you would expect about 2/3 of the actual page costs to be within Se of the predicted page costs, about 95% to be within 2Se, and so forth.

The sample mean plus or minus 1.96 times its standard error gives the following two figures: This is called the 95% confidence interval , and we can say that there is only a 5% chance that the range 86.96 to 89.04 mmHg excludes the mean of the population.

The relationship between two variables is generally considered strong when their r value is larger than 0.7. The correlation r measures the strength of the linear relationship between two quantitative variables.

If r< negative critical value or r> positive critical value, then r is significant. Since r=0.801 and 0.801>0.632, r is significant and the line may be used for prediction.

Compare r to the appropriate critical value in the table. If r is not between the positive and negative critical values, then the correlation coefficient is significant. Ifr is significant, then you may want to use the line for prediction.

The Correlation Coefficient When the r value is closer to +1 or -1, it indicates that there is a stronger linear relationship between the two variables. A correlation of -0.97 is a strong negative correlation while a correlation of 0.10 would be a weak positive correlation.

A p-value is the probability that the null hypothesis is true. In our case, it represents the probability that the correlation between x and y in the sample data occurred by chance. A p-value of 0.05 means that there is only 5% chance that results from your sample occurred due to chance.

The p-value, or probability value, tells you how likely it is that your data could have occurred under the null hypothesis. It does this by calculating the likelihood of your test statistic, which is the number calculated by a statistical test using your data.

statistically significant test result