{"id":558,"date":"2015-07-19T13:13:55","date_gmt":"2015-07-19T17:13:55","guid":{"rendered":"http:\/\/sites.berry.edu\/vbissonnette\/?page_id=558"},"modified":"2016-06-23T10:50:23","modified_gmt":"2016-06-23T14:50:23","slug":"regression","status":"publish","type":"page","link":"https:\/\/sites.berry.edu\/vbissonnette\/index\/stats-homework\/documentation\/regression\/","title":{"rendered":"Regression"},"content":{"rendered":"

Example homework problem:<\/h3>\n

You work for an automotive magazine, and you are investigating the relationship between a car’s gas mileage (in miles-per-gallon) and the amount of horsepower produced by a car’s engine. You collect the following data:<\/p>\n\n\n\n\n\n
Automobile:<\/td>\n1<\/td>\n2<\/td>\n3<\/td>\n4<\/td>\n5<\/td>\n6<\/td>\n7<\/td>\n8<\/td>\n9<\/td>\n10<\/td>\n<\/tr>\n
Horsepower:<\/td>\n95<\/td>\n135<\/td>\n120<\/td>\n167<\/td>\n210<\/td>\n146<\/td>\n245<\/td>\n110<\/td>\n160<\/td>\n130<\/td>\n<\/tr>\n
MPG:<\/td>\n37<\/td>\n19<\/td>\n26<\/td>\n20<\/td>\n24<\/td>\n30<\/td>\n15<\/td>\n32<\/td>\n23<\/td>\n33<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Compute the best-fitting regression line (Y’ = a + bx) for predicting a car’s gas mileage from its horsepower. Test to see if the slope of this regression line deviates significantly from zero (alpha = .05).<\/p>\n

If you would like some help with the hand-written solution to this problem, then click here<\/a>.<\/p>\n

\n

Enter these data into the first two columns of Stats Homework’s <\/i>data manager and rename the variables. Your screen should look like this:<\/p>\n

\"corr6\"<\/a><\/p>\n

Make sure to double-check and save your data. To conduct your analysis, pull down the Analyze<\/b> menu, choose Tests of Relationship<\/b>, and then choose Linear Regression<\/b>. You will be presented with\u00a0this dialog:<\/p>\n

\"reg17\"<\/a><\/p>\n

Select Horsepower as your X (predictor) variable, and then MPG as your Y (outcome) variable. \u00a0Then, check all the output options and click\u00a0Compute<\/strong>.<\/p>\n

Basic Output<\/h4>\n

\"reg18\"<\/a><\/p>\n

Descriptive Statistics<\/b>. Basic descriptive statistics are covered on the page for the explore procedure<\/a> and the correlation procedure<\/a>.<\/p>\n

Regression Equation<\/b>. Here, you will see a formal statement of your regression equation: Y’ = a + bx. As noted here, you will see that each predicted value of Y, and each error in prediction (residual) has been written back into your data set.<\/p>\n

Regression Parameters.<\/b>These statistics will help you understand whether or not your regression parameters –a and b– deviate significantly from zero.<\/p>\n