estimated simple linear regression equation

GATE CS Original Papers and Official Keys.

These videos investigate the linear relationship between people’s heights and arm span measurements. H a: The two variables are linearly related. H o: The two variables are not linearly related.

The variance of the distribution of the outcome is the same for all values of the predictor (assessed by visually checking a residual plot for a funneling pattern).The population of values for the outcome are normally distributed for each value of the predictor (assessed by confirming the normality of the residuals).The predictor variable and outcome variable are linearly related (assessed by visually checking a scatterplot).If run on the same data, a correlation test and slope test provide the same test statistic and p-value. Both analyses are t-tests run on the null hypothesis that the two variables are not linearly related. Inferential tests can be run on both the correlation and slope estimates calculated from a random sample from a population. This equation can also be used to predict values of Y for a value of X. Beyond giving you the strength and direction of the linear relationship between X and Y, the slope estimate allows an interpretation for how Y changes when X increases. The slope, b 1, is the average change in Y for every one unit increase in X. The intercept, b 0, is the predicted value of Y when X=0. A general form of this equation is shown below: A perfect linear relationship ( r=-1 or r=1) means that one of the variables can be perfectly explained by a linear function of the other.Ī linear regression analysis produces estimates for the slope and intercept of the linear equation predicting an outcome variable, Y, based on values of a predictor variable, X. If r is negative, then as one variable increases, the other tends to decrease.

If r is positive, then as one variable increases, the other tends to increase. The sign of r corresponds to the direction of the relationship. The further away r is from zero, the stronger the linear relationship between the two variables.

The Pearson correlation coefficient, r, can take on values between -1 and 1. A correlation analysis provides information on the strength and direction of the linear relationship between two variables, while a simple linear regression analysis estimates parameters in a linear equation that can be used to predict values of one variable based on the other. A correlation or simple linear regression analysis can determine if two numeric variables are significantly linearly related.

Estimated simple linear regression equation