Theory question 115
StatisticsThe table below shows the corresponding values of two variables X and Y.
X: 33, 31, 28, 25, 23, 22, 19, 17, 16, 14
Y: 4, 6, 4, 10, 12, 10, 14, 15, 18, 22
(a) Plot a scatter diagram to represent the data. (b) Calculate x̄, the mean of x and ȳ, the mean of y. (c) Draw the line of best fit to pass through (x̄, ȳ) (d) From your graph in (c), determine the (i) relationship between X and Y. (ii) value of Y when X is 24.
Show the model answer
(a) Plot the 10 points with X on the horizontal axis
(b) x̄ = 228/10 = 22.8, ȳ = 115/10 = 11.5
(c) Straight line through (22.8, 11.5) following the trend of the points
(d)(i) Negative linear relationship: Y decreases as X increases, roughly Y = 31.5 − 0.88X (gradient read from the graph about −0.9)
(ii) When X = 24, Y ≈ 10.4 (about 10–11 from the graph)
Find the gradient and intercept of your line of best fit to state the relationship.