Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

• Y−intercept is the y−coordinate of the point where the line crosses the y−axis. • Slope−intercept form is the equation y = mx + b where m, is the rate of change, or slope, and b is the initial value, or the y−intercept.

In the equation of a straight line (when the equation is written as “y = mx + b”), the slope is the number “m” that is multiplied on the x, and “b” is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the “slope-intercept form”.

The sample size is n=10, the degrees of freedom (df) = n-1 = 9. The t value for 95% confidence with df = 9 is t = 2.262.

If you want to be more than 95% confident about your results, you need to add and subtract more than about two standard errors. For example, to be 99% confident, you would add and subtract about two and a half standard errors to obtain your margin of error (2.58 to be exact)….Choosing a Confidence Level for a Population Sample.

In exploratory studies, p-values enable the recognition of any statistically noteworthy findings. Confidence intervals provide information about a range in which the true value lies with a certain degree of probability, as well as about the direction and strength of the demonstrated effect.

(b) P from CI for a ratio “exp” is the exponential function. The formula for P works only for positive z, so if z is negative we remove the minus sign. For a 90% CI, we replace 1.96 by 1.65; for a 99% CI we use 2.57.

The 95% confidence interval is providing a range that you are 95% confident the true difference in means falls in. Thus, the CI can include negative numbers, because the difference in means may be negative.

If the confidence interval does not contain the null hypothesis value, the results are statistically significant. If the P value is less than alpha, the confidence interval will not contain the null hypothesis value.

If the ratio equals to 1, the 2 groups are equal. Hence, if the 95% CI of the ratio contains the value 1, the p-value will be greater than 0.05. Alternatively, if the 95% CI does not contain the value 1, the p-value is strictly less than 0.05.

An RR of 1.00 means that the risk of the event is identical in the exposed and control samples. An RR that is less than 1.00 means that the risk is lower in the exposed sample. An RR that is greater than 1.00 means that the risk is increased in the exposed sample.

Layman’s. terms. Confidence Intervals. For a given statistic calculated for a sample of observations (e.g. the mean), the confidence interval is a range of values around that statistic that are believed to contain, with a certain probability (e.g.95%), the true value of that statistic (i.e. the population value).