Standard requirements for simple linear regression are satisfied.So you can better interpret the results obtained by this solver: A z-test for one proportion is a hypothesis test that attempts to make a claim about the population proportion (p) for a certain population attribute (proportion of males, proportion of people underage). That this approach is only appropriate when the Note: If you use this approach on an exam, you may also want to mention Less than the significance level (0.05), we cannot accept the Two-tailed test, "more extreme" means greater than 2.29 Having 99 degrees of freedom is more extreme than 2.29. The P-value is the probability that a t statistic SE is the standard error of the slope.Based on the N is the number of observations in the sample,ī 1 is the slope of the regression line, and We get the slope (b 1) and the standard error (SE)įreedom and the t statistic test statistic, The t statistic test statistic, and the P-value of the test Standard error of the slope, the slope of the regression Regression t-test to sample data, we require the To determine whether the slope of the regression line differs Significant, the slope will not equal zero. H a: The slope of the regression line is notĮqual to zero.If the relationship between home size and electric bill is
H o: The slope of the regression line is equal Null hypothesis and an alternative hypothesis. (3) analyze sample data, and (4) interpret results. (1) state the hypotheses, (2) formulate an analysis plan, The solution to this problem takes four steps: Home size? Use a 0.05 level of significance. Is there a significant linear relationship between annual bill and Output from a regression analysisĪnnual bill = 0.55 * Home size + 15 Predictor Coef SE Coef T P Constant 15 3 5.0 0.00 Home size 0.55 0.24 2.29 0.01 The following: annual electric bill (in dollars) and home size For each survey participant, the company collects The local utility company surveys 101 randomly selectedĬustomers. Typically, this involves comparing the P-value to theĪnd rejecting the null hypothesis when the P-value is less than The null hypothesis, the researcher rejects the null hypothesis. If the sample findings are unlikely, given To assess the probability associated with the test statistic. Sample statistic as extreme as the test statistic. The P-value is the probability of observing a The test statistic is a t statisticī 1 is the slope of the sample regression line, and For simple linear regression (one independentĭF = n - 2where n is the number of observations in the sample. The regression line will be provided by most statistics X is the mean of the independent variable, X i is the observed value of the independent variable for Ŷ i is estimated value of the dependent variable X) 2 ]where y i is the value of the dependent variable for If you need to calculate the standard error of the slope
However, other software packages might use aĭifferent label for the standard error. In this example, the standard error is referred toĪs "SE Coeff". Predictor Coef SE Coef T P Constant 76 30 2.53 0.01 X 35 20 1.75 0.04In the output above, the standard error of the slope (shaded in gray) The table below shows hypothetical output for the following Standard error of the slope as a regression analysis Many statistical software packages and some graphing calculators Sample problem at the end of this lesson. The approach described in this section is illustrated in the Test statistic, and the P-value associated with the test statistic. Standard error of the slope, the slope of the regression line, the (2) formulate an analysis plan, (3) analyze sample data, and The test procedure consists of four steps: (1) state the hypotheses,
How to verify that regression requirements are met.
Β 1 is the slope (also called the regression coefficient), Whether there is a significant linear relationship betweenĪn independent variable X and a dependent variable This lesson describes how to conduct a hypothesis test to determine AP stat formulas Hypothesis Test for Regression Slope.Confidence interval Confidence intervals.Simulation of events Discrete variables.Diff between means Statistical InferenceĪP Statistics: Table of Contents The basics.Experimental design Anticipating Patterns.