Exam 7: Linear Regression

Using advertised prices for used Ford Escorts a linear model for the relationship between a car's age and its price is found.The regression has an $\mathrm { R } ^ { 2 }$ = 88.2%.Describe the relationship

Ten Ford Escort classified ads were selected.The age and prices of several used Ford Escorts are given in the table. Age (years) Price 1 \ 10,000 2 \ 8500 2 \ 8000 3 \ 6000 3 \ 5900 4 \ 5800 4 \ 5000 5 \ 3000 6 \ 2000 6 \ 1900

A golf ball is dropped from 15 different heights (in cm)and the height of the bounce is recorded (in cm.)The regression analysis gives the model $\hat{\text { bounce }} = - 0.3 + 0.69$ drop.Explain what the slope of the line says about the bounce height and the drop height of the ball.

When checking the "Does the Plot Thicken?" condition,which is the best graph to look at?

A biology student does a study to investigate the association between the amount of sunlight and the number of roses on a rosebush in one summer.(The $\mathrm { R } ^ { 2 }$ value is 58%)He claims that the amount of sunlight determines 58% of the number of roses on a rosebush in one summer.

A random sample of records of electricity usage of homes gives the amount of electricity used in July and size (in square feet)of 135 homes.A regression was done to predict the amount of electricity used (in kilowatt-hours)from size.Suppose the linear model is appropriate.Do you think the slope is positive or negative? Why?

If the linear correlation between typical daily temperature and coat sales is -0.737 and today the temperature is 2 standard deviations above the mean,what would you predict coat sales to be with respect to its mean?

The relationship between the number of games won by an NHL team and the average attendance at their home games is analyzed.A regression analysis to predict the average attendance from the number of games won gives the model $\hat{\text { attendance }} = - 3000 + 176$ wins.One team averaged 4240 fans at each game.They won 57 times.Calculate the residual and explain what it means.

A golf ball is dropped from 15 different heights (in cm)and the height of the bounce is recorded (in cm).The regression analysis gives the model $\hat{\text { bounce }} = 0.5 + 0.71$ drop.A golf ball company is trying to show that its new ball will increase your driving distance.If the new ball is dropped from several heights would the company rather see positive or negative residuals.Explain.