Linear Regression, Hypothesis Testing and Probability

1. The basic assumption in linear regression is that the relationship between variables can be approximated by linear relation. Can you think of examples of such relations that you expect to be linear relations?

2. Pick one of the feature hypothesis tests and explain it in everyday language.

3. Consider rolling a pair of dice. What is the probability of rolling two faces such that their sum is an odd number or 3 is one of the faces?

4. Assume that the probability of the number of breakdowns of a cell phone of a certain make in the first year of service is a Poisson distribution and the standard deviation of that distribution is 2. What is the probability that a phone of that make will break down between 2 and 4 times in the first year of service.

5. The following is a list pairs of numbers consisting of amounts invested in recent movies (in millions) and the revenues generated by the movies. (2,2), (4,5), (6,7), (18,15), (20,18), (24,30). Calculate the regression equation for the data and the correlation coefficient. Is there good evidence of a linear relation between investment and revenue?

Solution Summary

This solution gives examples of linear regression in a company's profit equation, provides a null and alternative hypothesis and also calculates the probability of the cell breakdown, regression equation and correlation coefficient. All steps are shown in a clear manner with brief explanations.

... general, in most practical hypothesis-testing situations, the ... 0.65 indicates a stronger linear relationship between ... points about a fitted regression line, the ...

... In a simple linear regression equation, to determine ... existence of a significant linear relationship between ... variable 'Y' a hypothesis test concerning whether ...

T Test, Linear Equations and linear regression. ... two tail p value was in fact 0.33 then since we only want to test (alternative hypothesis) for one ...

... (Form the hypotheses, show the ... t=(6.5-6)/(1.5/sqrt(25))=1.67 Since 1.67<1.71, we could not reject the null hypothesis. ... Use the simple linear regression model. ...

... carry out a chi-square test of independence, in the alternative hypothesis we state ... The slope of the simple linear regression equation represents ...

... would the values of this table be interpreted in terms of linear regression? ... The null hypothesis tested is H0: Mean life of a battery for a cell phone ...

... of significance to conduct your hypothesis test, please explain ... rate can be assessed by testing the slope ... use the estimated simple linear regression model for ...

... a test, and the two kinds of errors associated with testing. ... occurs when one does not reject the null hypothesis when it ... 4) What is simple linear regression? ...

... 529 11.5 3.01 118 1.8553 2812 71.95 The general form of simple linear regression is Y ... The regression equation = Y = 21.11*X+10.88. ... The alternative hypothesis is. ...

... What is the slope of the linear equation? ... method for the calculation of testing of hypothesis, probability, confidence interval and regression analysis ...