or

or

∑

∑

∑

∑

∑

xi yi

= 44328.69

xi −HSA

= 44328.69

x i2−HSA yi −GPA

= 1135204

= 591.01

yi2 −GPA

= 1799.43

n = 200 r= r=

∑

xi yi

−(∑ x )(∑ y ) / n i i

2

"

∑ xi 2 −(∑ xi ) / n%"∑ yi 2 −(∑ yi ) / n%

$

'$

'

#

&#

&

2

44328.69 − (14734)(591) / 200

"1135204 − (44328.69) 2 / 200$"1799.43− (591) 2 / 200$

#

%#

%

= 0.48437

b. Correlation between English ACT scores and GPA (15 points) • Use can use the excel function CORREL (data colum1, data column2) or minitab

∑

∑

∑

∑

∑

xi yi

= 13849.35

= 4634

xi −ENG x i2−ENG yi −GPA y i2−GPA

n = 200

= 110612

= 591.01

= 1799.43

∑

r=

xi yi

−(∑ x )(∑ y ) / n i i

2

2

"

%"

%

2

2

$∑ xi −(∑ xi ) / n'$∑ yi −(∑ yi ) / n'

#

&#

&

13849.35− (4634)(591) / 200

"110612 − (4634) 2 / 200$""1799.43− (591) 2 / 200$$

#

%##

%%

r=

= 0.37594181

Correlation between Math ACT scores and GPA Use can use the excel function CORREL (data colum1, data column2) or minitab

∑

∑

∑

∑

∑

xi yi

= 14051.28

xi −MATH x i2−MATH yi −GPA

= 4713

= 114095

= 591.01

yi2 −GPA

= 1799.43

n = 200

∑

r=

xi yi

−(∑ x )(∑ y ) / n i i

2

"

∑ xi 2 −(∑ xi ) / n%"∑ yi 2 −(∑ yi ) / n%

$

'$

'

#

&#

&

2

14051.28 − (4713)(591) / 200

"114095− (4713) 2 / 200$"1799.43− (591) 2 / 200$

#

%#

%

r=

= 0.310100412

Correlation between Comp ACT scores and GPA Use can use the excel function CORREL (data colum1, data column2) or minitab

∑

∑

∑

∑

∑

xi yi

= 14173.71

xi −COMP x i2−COMP

= 114676

= 591.01 y −GPA i y i2−GPA

n = 200

= 4748

= 1799.43

r=

r=

∑

xi yi

−(∑ x )(∑ y ) / n i i

2

2

"

%"

%

2

2

$∑ xi −(∑ xi ) / n'$∑ yi −(∑ yi ) / n'

#

&#

&

14173.71− (4748)(591)