University:
McMaster University
Course:
STATS 1LL3 | Introduction to Probability and Statistics
Academic year:

2023
Views:

262

Pages:

3
Author:

Sabrina S.

Video 24: Testing for a linear relationship ya + bx •y is the dependent variable •x is the independent variable band a are regression coefficients Is there a linear relationship between x and y? The true (population) correlation is often unknown so we use evidence of correlation measured in a sample to infer that of the population. P population correlation (parameter) sample correlation (statistic) 1 r falls on this scale 0 1 perfect negative high negative Independent louw positive perfect positive high pasitive how negative as x increases, y increases as x increases, y decreases R measures the proportion of the variation in (often expressed as a percentage) y that X is able to explain. So the higher the value of relationship between X and (or 2), the closer (stronger) the y mtercept + Bx Slope of straight line Parameters a and B regression coefficients Statistics a and b estimates of a and ẞ (random variables) Note a is the intercept porameter, not to be confused with level of significance In general, we are more interested in testing hypotheses about B (slope of straight Ime) than a (y-intercept) If BO then there is ro linear relationship between x and y So we can use this os a basis for testing whether or not there is a linear relationship between x and y Step 1 → Ho Bo we assume no relationship step 2 → OF or Step 3 이 step 4 rejection region under assumption of Ho the test statistic has a t-distribution with 1-2 df. ne the number of pairs of observationg test statistic tn-2 we will reject Ho if our test statistic falls within the region that defines the 1% most extreme points of t-z distribution. For two-sided test reject Ho if Test Statistic > 0.009 tn-2 0.01 For a For a test reject Ho if Test Statistic tn-z 이 step S test stat observed statistic (b) hypothesised parameter (B) b-0 SE Standard enor of (b) Step 6 if test stot falls in rejection region reject Ho the modified approach we assume no relationship between x and y 2) H1 +0 3 ) read from excel output the test statistic = 51.97 (in excel example) 4) read from excel output the p-value 2 x 10- 5.) conclusion based on the p-value (approximately o) we reject Ho and conclude that there is a relationship between year mark and final mark We can use the regression line to predict a value of y from a given value X. eg if year mark (x)。 3.0635 + 44.12 50% then final mark (y)=44.12% (0.8211) (50) The value of the correlation coefficient, when squared, (r) can be used to indicate the proportion of variation in y thot X. is able to explain.