Testing Regression Coefficients Prepared by: Bhakti Joshi February 06, 2012

Hypothesis Testing: t-Test … Testing whether there is a linear relationship between an independent variable ‘X’ and a dependent variable ‘Y’ Null Hypothesis Alternate Hypothesis Test (t) Statistic Critical Region States no difference between the two variables. Denoted by H 0 States that there is difference between the two variables. Denoted by H 1 Sample or a calculated number that is used to determine whether a hypothesis will be accepted or rejected Is the set of all outcomes which causes null hypothesis to be rejected in favour of the alternative hypothesis

Testing Regression Coefficients Y i = α + β X i + ε i H 0 : β = 0H 1 : β ≠ 0 β Standard Error (s.e.) t-statistic = Standard Error (s.e.) = Sqrt Σ (Yi – Y) 2 (n – k) ᶺ Sqrt (X i – X ) 2

Critical Region Critical region is the rejection region, where the null hypothesis is rejected Degrees of Freedom (df) Confidence Interval Critical Value df = n - k, where n equals number of observations and k equals number of variables in the regression equation df helps to understand the space available across data points for reflecting the presumed relationship between X and Y variables Used to describe the amount of uncertainty associated with a sample estimate of a population parameter For example, 95% confidence interval implies that we are 95% confident that the null hypothesis can be rejected A value determined from df and confidence interval that should be less than the test- statistic in order to reject the null hypothesis Also known as a cutoff value

Testing Regression Coefficients t-statistic > t-critical value, reject null hypothesis (H 0 ). ‘β' is significant t-statistic < t-critical value, do not reject the null hypothesis (H 0 ). ‘β’ is not significant

Problem 1 Year R&D Expens e in Rs crore (X) Annual Profit in Rs. Crore (Y) Y Yi - Y(Yi – Y) ᶺ ᶺᶺ 42 α = 20 β = 2 df = 4 Find test statistic?

Problem 2 For n=4, the slope is 0.75 and y-intercept is calculate the test-statistic and determine whether the null hypothesis can be accepted or rejected H 0 : β = 0

Problem 3 Number of advertisements Number of Coke Cans purchased

Topics for Finals Measures of Central Tendency Measures of Dispersion Skewness, Kurtosis and its Applications Correlation Coefficient Regression Analysis Time Series Probabilities and Probability distribution Index Numbers

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