The following shows the regression formulas for each type of regression. Use the same key operations as linear regression to recall results for these types of regression. Logarithmic, Exponential, Power, and Inverse Regression Finally, calculate the coefficient of determination (r 2) and sample covariance ( ∑ xy - n∙ x -∙ y - n - 1).Įach time you press to register your input, the number of data input up to that point is indicated on the display ( n value).Ĭoefficient of Determination = 0.965517241 Next, use the regression formula to estimate atmospheric pressure at -5☌ and temperature at 1000 hPa.
▶Permutation (nPr) and Combination (nCr).
▶Random Integer (RanInt#) (fx-220 PLUS only).▶Rectangular-Polar Coordinate Conversion.▶Power Functions and Power Root Functions.▶Exponential Functions, Logarithmic Functions.▶Hyperbolic Functions, Inverse Hyperbolic Functions.▶Trigonometric Functions, Inverse Trigonometric Functions.Natural Logarithm Base e (fx-82MS/fx-85MS/fx-300MS/fx-350MS only).Converting Values between Sexagesimal and Decimal.▶Degree, Minute, Second (Sexagesimal) Calculations.Mixed Fraction ↔ Improper Fraction Conversion.Number of Decimal Places and Number of Significant Digits.Initializing the Calculation Mode and Other Settings.Hypothesis testing can be done using our Hypothesis Testing Calculator.(2nd edition / S-V.P.A.M.) Before Using the Calculator The two tests for signficance, t test and F test, are examples of hypothesis tests. One of the most important parts of regression is testing for significance. This is known as multiple regression, which can be solved using our Multiple Regression Calculator. However, we may want to include more than one independent vartiable to improve the predictive power of our regression. In a simple linear regression, there is only one independent variable (x). Confidence intervals will be narrower than prediction intervals. A prediction interval gives a range for the predicted value of y. The differennce between them is that a confidence interval gives a range for the expected value of y. In both cases, the intervals will be narrowest near the mean of x and get wider the further they move from the mean. t TestĬonfidence intervals and predictions intervals can be constructed around the estimated regression line. The only difference will be the test statistic and the probability distribution used. In simple linear regression, the F test amounts to the same hypothesis test as the t test. The test statistic is then used to conduct the hypothesis, using a t distribution with n-2 degrees of freedom. So, given the value of any two sum of squares, the third one can be easily found. The relationship between them is given by SST = SSR + SSE. Before we can find the r 2, we must find the values of the three sum of squares: Sum of Squares Total (SST), Sum of Squares Regression (SSR) and Sum of Squares Error (SSE). The coefficient of determination, denoted r 2, provides a measure of goodness of fit for the estimated regression equation. The graph of the estimated regression equation is known as the estimated regression line.Īfter the estimated regression equation, the second most important aspect of simple linear regression is the coefficient of determination. The formulas for the slope and intercept are derived from the least squares method: min Σ(y - ŷ) 2. There are two things we need to get the estimated regression equation: the slope (b 1) and the intercept (b 0). Furthermore, it can be used to predict the value of y for a given value of x. It provides a mathematical relationship between the dependent variable (y) and the independent variable (x). In simple linear regression, the starting point is the estimated regression equation: ŷ = b 0 + b 1x.