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
   •   In the space below, use technology to construct a scatterplot of the bivariate data set.




   •   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?



   •   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?

   •   Predict the 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.


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


Answer 1

am using excel to answer these questions

firstly I will answer question-b

r=-0.97148

r value always lies between -1 and +1

r is between 0 and 1 ----- positive correlation

r is between 0 and -1------negative correlation

when r=1 then there is an exact positive correlation between variables

when r=-1 then there is an exact negative correlation between variables

here our r value equals to -0.97148--indicates a strong negative correlation

question-c

here slope is -0.826

therefore as the value of X increases by one the value of decreases by 0.826

question-d

y=-0.826*63+70.39------->Y=18.352

question-e

23=-0.826*X+70.39----------->X=57.373

qoestion-f

this implies that 94.3% of the variance in the  miles per gallon of the automobile is explained by the average speed of a car