Question

An educator wants to see how the number of absences for a student in her class affects the student’s final grade. The data obtained from a sample are shown.

No. of absences x	10	12	2	0	8	5
Final grade y	70	65	96	94	75	82

Based on the above data, answer the following questions with the appropriate rounding. Use complete sentences to answer questions.

1. Find r

2. Characterize r

3. Find r²

4. Interpret r²

5. Find the least square regression equation.

6. Find the standard error of estimate and describe what the number says.

7. Find the prediction for the final grade when a student has 7 absences.

Find the prediction for the final grade when a student has 15 absences

Answer 1

	X	Y	X * Y	X2	Y2	Ŷ	( Y - Ŷ )2
	10	70	700	100	4900	70.1072	0.0115
	12	65	780	144	4225	64.7718	0.0521
	2	96	192	4	9216	91.4487	20.714
	0	94	0	0	8836	96.7841	7.7511
	8	75	600	64	5625	75.4426	0.1959
	5	82	410	25	6724	83.4456	2.0899
Total	37	482	2682	337	39526	482	30.815

r = -0.981

r represent the strength of correlation between two variables.

Coefficient of Determination
R² = r² = 0.962
Explained variation = 0.962* 100 = 96.2%

r² Implies the % of variation in dependent variable explained by independent variable.

Equation of regression line is Ŷ = a + bX


b = -2.6677
a =( Σ Y - ( b * Σ X) ) / n
a =( 482 - ( -2.6677 * 37 ) ) / 6
a = 96.7841
Equation of regression line becomes Ŷ = 96.7841 - 2.6677 X

Standard Error of Estimate S = √ ( Σ (Y - Ŷ ) / n - 2) = √(30.8147 / 4) = 2.7755

When X = 7
Ŷ = 96.784 + -2.668 X
Ŷ = 96.784 + ( -2.668 * 7 )
Ŷ = 78.11

When X = 15
Ŷ = 96.784 + -2.668 X
Ŷ = 96.784 + ( -2.668 * 15 )
Ŷ = 56.76