Question

An individual wanted to determine the relation that might exist between speed and miles per gallon of an automobile. Let X be the average speed of a car on the highway measured in miles per hour and let Y represent the miles per gallon of the automobile. The following data is collected:

X	50	55	55	60	60	62	65	65
Y	28	26	25	22	20	20	17	15

a. In the space below, draw a scatterplot of the bivariate data set.

b. What is the value for r? Interpret this value, would you say that the correlation is positive or negative? Strong or Weak? How do you know?

c. From the regression equation given above, what value is the slope of the line? Interpret this slope, what does it tell us about the relationship between average speed and miles per gallon?

d. Predict the miles per gallon of a car traveling 63 miles per hour.

e. Predict the average speed of a car whose fuel mileage is 23 miles per gallon.

f. Find r squared. What does this statistic tell us about between average speed and miles per gallon?

Answer 1

a. Scatter plot:

Bring data in to excel sheet. Select bot X and Y data set and go to data tab , choose scatterplot diagram.

b. r value

r value is nothing but correlation coefficient

r = -0.97

it is perfect negative correlation and weak

c. regression equation:

y = -0.8265x + 70.39

Select any data point in the chart and right click--> add trend line. choose "Linear" trend and select display an equation option

what value is the slope of the line?

y = -0.8265x + 70.39

this tells us if there is a relationship between the two variables. The scatter plot can show that a relationship can exist but not always prove that the variables are causing the other.

d. Predict the miles per gallon of a car traveling 63 miles per hour

y = -0.8265x + 70.39

x = 63

y = 18.3205

so 19 MPG is the predicted miles per gallon of a car traveling 63 miles per hour

Predict the average speed of a car whose fuel mileage is 23 miles per gallon.

Same way create scatterplot

y = -1.1419x + 83.693

=-1.1419*23+ 83.69 = 57.4293

58 MPG is the the average speed of a car whose fuel mileage is 23 miles per gallon.

Find r squared. What does this statistic tell us about between average speed and miles per gallon?

R-squared = 0.9438 = 0.94 (round to two decimal value)

This tells us how close the data are from fitting the regression line, which is also known as the coefficient of determination. It is the percentage of the response variable variation that is explained by the linear model.