Is that there is no significant linear correlation. So, another way of writing the null hypothesis Then you get a horizontal line at the mean of the y variable. In the model since it is multiplied by zero. If the coefficient is zero, then the variable (or constant) doesn't appear H 0: β 0 = 0 and the null hypothesis for the snatch row is that the coefficient is zero, The null hypothesis for the constant row is that the constant is zero, that is The b 0 and b 1 are just estimates for β 0 and β 1. The model for the regression equation is y = β 0 + β 1 x + ε where β 0 is the population parameter for the constant and the β 1 is the population parameter for the slope and ε is the residual or error term. Speaking of hypothesis tests, the T is a test statistic with a student's t distributionĪnd the P is the p-value associated with that test statistic.Įvery hypothesis test has a null hypothesis and there are two of them here since Need to concern ourselves with formulas for it, but it is useful in constructingĬonfidence intervals and performing hypothesis tests. The "SE Coef" stands for the standard error of the coefficient and we don't really On snatch of 0.9313 is the slope of the line. Theĥ4.61 is the constant (displayed as 54.6 in the previous output) and the coefficient The "Coef" column contains the coefficients from the regression equation. Let's go through and look at this information and how it ties into the ANOVAĪ quick note about the table of coefficients, even though that's not what we're The method you would go through to find the equation of the regression equation In calculations, so we'll go with Minitab's output from here on, but that's Ours is off a little because we used rounded values Notice that the regression equation we came up with is pretty close to Here is the regression analysis from Minitab. So we can write the regression equation as clean = 54.47 + 0.932 snatch. Solving for b 0 gives the constant of 54.47. Variables into the regression equation and solving for b 0.
The y-intercept, b 0, is found by substituting the slope just found and the means of the two Since the best fit line always passes through the centroid of the data, The formula for the slope is b 1 = r (s y / s x).įor our data, that would be b 1 = 0.888 ( 17.86 / 17.02 ) = 0.932. The following explanation assumes the regression equation is y = b 0 + b 1x.
Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Our predictor (x) variable is snatch and our response variable (y) is clean. Let's start off with the descriptive statistics for the two variables. No linear correlation and say that there is significant positive linear correlationīetween the variables. Hypothesis is true and so in this case we'll reject our null hypothesis of The p-value is the chance of obtaining the results we obtained if the null The null hypothesis here is H 0: ρ = 0, that is, that there is no significant linear correlation. Test, and every time you have a hypothesis test, you have a null hypothesis. Every time you have a p-value, you have a hypothesis Remember that number,įor now, the p-value is 0.000. The Pearson's correlation coefficient is r = 0.888. Pearson correlation of snatch and clean = 0.888 On to finding the correlation coefficient. The clean & jerk and the snatch weights for the competitors, so let's move You can see from the data that there appears to be a linear correlation between The first rule in data analysis is to make a picture. Jerk lift Total The total weight (kg) lifted by the competitor Age Body The weight (kg) of the competitor Snatch The maximum weight (kg) lifted during the three attempts at a snatch lift Clean The maximum weight (kg) lifted during the three attempts at a clean and Data Dictionary Age The age the competitor will be on their birthday in 2004. Kg) that men who weigh more than 105 kg were able to lift are given in the We will use a response variable of "clean" and a predictor variable of "snatch". In the snatch event and what that same competitor can lift There is a correlation between the weights that a competitive lifter can lift The data used here is from the 2004 Olympic Games.