The relationship between the x and y variables in the scatter plot is
approximately linear.
(a) Increase in the y-variable follows from an increase in the x-variable
(b) The regression coefficient is approximately 0.9465
(c) The slope of the regression line is 2.5
(d) The equation of the regression line is approximately; y = 2.5·x + 10.5
(e) If x = 25, the value of y is 73
Reasons:
(a) From the attached graph, we have;
The increase in the x-variable gives a corresponding increase in the y-
variable.
(b) The correlation coefficient is given by plotting the given points using
MS Excel and finding the regression line, from which we have;
The regression coefficient is R ≈ √(0.8958) ≈ 0.9465
(c) The slope of the regression line is given by the slope of the line with
points (7, 28), and (9, 33), as follows;
[tex]Slope = \dfrac{33 - 28}{9 - 7} = 2.5[/tex]
The slope of the regression line is approximately 2.5
(d) Using the slope, m = 2.5, we get;
Equation of regression line, is y - 33 = 2.5·(x - 9)
Which gives;
y - 33 = 2.5·(x - 9) = 2.5·x - 22.5
y = 2.5·x - 22.5 + 33 =
The equation of the line is; y = 2.5·x + 10.5
(e) If x = 25, we have;
y = 2.5 × 25 + 10.5 = 73
Therefore, if x = 25, y = 73
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