Question

12. A study is conducted concerning automobile speeds and fuel consumption rates. The following data is collected:                                              

   X Speed   45        52         49         60         67         61        

  Y MPG    22         26         21         28         33         32        

                                                                                                                                 

1.    Draw Scatter plot
2. Compute the coefficient of correlation, and make a comment about that.
3. Compute the coefficient of determination, and make a comment about that.
4. Compute the coefficient of Non- determination, and make a comment about that.
5. Find Regression Line and make a comment about that. Also, at what location the line crosses    the y-axis.
6. What is the “Residual’ at speed of 60?
7.    What is the predicted fuel consumption at speed of 75 mph.

8. Determine at the 0.05 significance level whether the correlation in the population is greater than zero.

Answer 1

Dear student, we can answer only four subparts at a time, please help to upload other parts separately.

a)

b)

The coefficient of correlation comes out to be 0.944(shown in excel).

It is a strong positive correlation, which means an increase in X leads to an increase in Y and vice-versa.

c)

The coefficient of determination comes out to be 0.89. It means 89% of the variation in Y can be explained by the variation in X.

d)

coefficient of non-determination = 1 - coefficient of determination = 1 - 0.89 = 0.11

The coefficient of Non-Determination explains the amount of unexplained, or unaccounted for, the variance between two variables, or between a set of variables (predictors) in an outcome variable. Where the Coefficient of Non-Determination is simply 1 – R2.

11% of the unexplained variation in Y is present, it can not be determined.

e)

We will be applying the Linear regression model here, it can be done by using the function LINEST(y_value, x_value, TRUE, TRUE) where y_values contain values of X here and x_values have Y values.

Select 5 rows and 2 columns and then write the formula in the first cell and after that, press Shift + Ctrl + Enter.    

The equation comes out to be -

Y = -4.41 + 0.56*X