Question

The following information was collected on 20 randomly chosen high school students, which compared their IQ score to musical aptitude.

Row IQ Score Mus.Apt.
1 95 30
2 106 37
3 110 35
4 104 28
5 98 17
6 114 45
7 123 33
8 100 18
9 98 24
10 88 18
11 102 30
12 105 30
13 111 32
14 106 33
15 110 38
16 143 42
17 106 40
18 98 20
19 104 23
20 97 25
Descriptive Statistics
Variable N Mean Median TrMedian StDev SEMean
IQ Score 20 105.90 104.50 104.83 11.60 2.59
Mus.Apt 20 29.90 30.00 29.78 8.27 1.85
Variable Min Max Q1 Q2
IQ Score 88.00 143.00 98.00 110.00
Mus.Apt 17.00 45.00 23.25 36.50
Regression Analysis
Predictor Coef Stdev t-ratio p
Constant -22.26 12.94 -1.72 0.102
IQ Score 0.4925 0.1215
s= 6.143 R-sq= 47.7% R-sq(adj)= 44.8%
A. What is the equation of the least squares regression line that would be used to predict musical aptitude from an IQ score? Be sure to define any variables used.
B. Calculate and interpret a 95% confidence interval for the slope of the regression line.
C. Is there a significant relationship between IQ score and musical aptitude? Give a statistical justification to support your answer. Assume conditions for regression inference are satisfied. Test at
α=0.05.

Answer 1

Y = 0.4925X - 22.26 ;

(-12.413, 13.398) ;

Yes, there is

Explanation:

X = IQ Score ; Y = musical aptitude

The regression equation from the table given using the slope and intercept coefficient :

Y = 0.4925X - 22.26

0.4925 = slope ; Intercept = - 22.26

The 95% confidence interval of the slope :

Confidence interval = b ± Tcritical*SE

Tcritical at 95%, df = n - 2 = (20 - 2) = 18

Tcritical = 2.1009

b = slope Coefficient = 0.4925

S.E = 6.143

Hence, we have :

Confidence interval = 0.4925 ± (2.1009 * 6.143)

Confidence interval = 0.4925 ± 12.9058287

Lower boundary = 0.4925 - 12.9058287 = - 12.413

Upper boundary = 0.4925 + 12.9058287 = 13.398

(-12.413, 13.398)

There is a significant relationship between IQ score and musical aptitude because, 0 is within the confidence interval obtained.