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Curvilinear Regression - SAGE Research Methods

Because the P-value is so small (less than 0.001), we can reject the null hypothesis and conclude that β does not equal 0. There is sufficient evidence, at the α = 0.05 level, to conclude that there is a relationship in the population between skin cancer mortality and latitude.

Explanatory Analysis A method of inquiry that focuses on the formulating and testing of hypotheses.
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There are six possible outcomes whenever we test whether there is a linear relationship between the predictor x and the response y, that is, whenever we test the null hypothesis H : β = 0 against the alternative hypothesis H : β≠ 0.

Curvilinear Regression In: Encyclopedia of Measurement and Statistics

Again, we follow standard hypothesis test procedures. First, we specify the null and alternative hypotheses:
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The test for the significance of regression, for the regression model obtained for the data in the table (see ), is illustrated in this example. The null hypothesis for the model is:

If you are mainly interested in using the P value for hypothesis testing, to see whether there is a relationship between the two variables, it doesn't matter whether you call the statistical test a regression or correlation. If you are interested in comparing the strength of the relationship (r2) to the strength of other relationships, you are doing a correlation and should design your experiment so that you measure X and Y on a random sample of individuals. If you determine the X values before you do the experiment, you are doing a regression and shouldn't interpret the r2 as an estimate of something general about the population you've observed.

Curvilinear regression is the regression in …

We accept the Null Hypothesis and Reject the Alternate hypothesis We are 95 ..
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Third, we use the resulting test statistic to calculate the P-value. Again, the P-value is the answer to the question "how likely is it that we’d get a test statistic t* as extreme as we did if the null hypothesis were true?" The P-value is determined by referring to a t-distribution with n-2 degrees of freedom.

Finally, we make a decision. If the P-value is smaller than the significance level α, we reject the null hypothesis in favor of the alternative. If we conduct a "two-tailed, not-equal-to-0" test, we conclude "there is sufficient evidence at the α level to conclude that the mean of the responses is not 0 when x = 0." If the P-value is larger than the significance level α, we fail to reject the null hypothesis.

If it is known that a simple linear regression model ..
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If anANOVA test is conducted and the null hypothesis is rejected, ..

where is the regression mean square and is the error mean square. If the null hypothesis, , is true then the statistic follows the distribution with degrees of freedom in the numerator and ( ) degrees of freedom in the denominator. The null hypothesis, , is rejected if the calculated statistic, , is such that:

we fail to reject the null hypothesis and ..

Dividing the estimated coefficient 389.19 by the estimated standard error 23.81, Minitab reports that the test statistic is 16.34. By default, the P-value is calculated assuming the alternative hypothesis is a "two-tailed, not-equal-to-0" hypothesis. Upon calculating the probability that a t random variable with n-2 = 47 degrees of freedom would be larger than 16.34, and multiplying the probability by 2, Minitab reports that is 0.000 (to three decimal places). That is, the P-value is less than 0.001.


The test for significance of regression in the case of multiple linear regression analysis is carried out using the analysis of variance. The test is used to check if a linear statistical relationship exists between the response variable and at least one of the predictor variables. The statements for the hypotheses are:

Curvilinear Regression and Correlation

Because the P-value is so small (less than 0.001), we can reject the null hypothesis and conclude that β does not equal 0 when x = 0. There is sufficient evidence, at the α = 0.05 level, to conclude that the mean mortality rate at a latitude of 0 degrees North is not 0. (Again, note that we extrapolated in order to arrive at this conclusion.)

This can refer to linear or curvilinear regression

The test is used to check the significance of individual regression coefficients in the multiple linear regression model. Adding a significant variable to a regression model makes the model more effective, while adding an unimportant variable may make the model worse. The hypothesis statements to test the significance of a particular regression coefficient, , are:

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