Student Quiz Grades Test Grades 1.Describe the association between Quiz Grades and Test Grades. 2.Write the equation of the line of regression. 3.Use this model to predict a test grade based on a quiz grade of What is the Residual for the quiz grade of 82? 5.Is this a good model? Quiz Grade Test Grade Quiz Grade Residuals Test Grade = (Quiz Grade) = (82) WARM – UP r = Resid=y – y Resid= Resid=1.974

H 0 : β 1 = 0 A Linear Relationship does NOT exist H a : β 1 ≠ 0 A Linear Relationship does exist True Slope of the linear relationship.

Regression Output Analysis

WARM – UP The Statistics had an average of 81.2 with a standard deviation of 4.5. a.) What score represents the 90 th percentiles? b.) What is the probability that at least 3 out of 8 randomly selected students scored in the top 10%. c.) Assuming a Normal Distribution, what is the probability that a random sample of 3 students will have a mean score of at least 85? z = InvNorm(0.90) =1.282 x = = Prob. = Normalcdf(1.463,∞) =0.0718

WARM – UP Many Economist believe that the down turn of the US Economy is due to developments in the Housing Market. The table below indicates random Medium home prices and the Unemployment Rate at that time. 3/076/0710/0712/075/087/0811/081/ DATE Housing $100K Unemployment Rate 1.Describe the association between Housing values and Unemployment. 2.Write the equation of the line of regression. 3.Use this model to predict unemployment if housing reaches $180, Is this a good model?

3/076/0710/0712/075/087/0811/081/ DATE Housing $100K Unemployment Rate 1.Describe the association between Housing values and Unemployment. 2.Write the equation of the line of regression. 3.Use this model to predict unemployment if housing reaches $180, Is this a good model? Housing $100K Unemployment Housing $100K Residuals Unemployment = – 0.054(Housing $K) = – 0.054(180) =

LINEAR REGRESSION t – TEST # Hours of Study Test Grade Does a significant relationship exist between number of hours studying and test grades? H 0 : β 1 = 0 H a : β 1 ≠ 0

Chapter 27 – INFERENCE FOR REGRESSION –Spread around the line = s e –Spread around the line = s e : s eThe spread around the line is measured with the standard deviation of the residuals s e.

Chapter 27 – INFERENCE FOR REGRESSION –Spread of the x values = s x –Spread of the x values = s x : A large standard deviation of x provides a more stable regression.

–Spread around the line = s e –Sample Size = n –Spread of the x values = s x SE(b 1 ) is the Standard Error about the slope.

β = 0 A Linear Relationship does NOT exist β ≠ 0 A Linear Relationship does exist LINEAR REGRESSION t – TEST Used to determine whether a significant relationship exists between two quantitative variables.

WARM – UP Many Economist believe that the current situation of the US Economy is due to developments in the Housing Market. The table below indicates random Medium home prices and the Unemployment Rate at that time. 3/076/0710/0712/075/087/0811/081/ DATE Housing $100K Unemployment Rate Dependent Variable is: URate R-squared = 68.1% s = with 8 – 2 = 6 degrees of freedom Variable Coefficient SE(Coeff) T-ratio P-Value Intercept Housing = b 1 = SE(b 1 )

Chapter 27 – INFERENCE FOR REGRESSION –Sample Size = n –Sample Size = n: Having a larger sample size, n, gives more consistent estimates.