6

The scores obtained by a group of students in tests that measure verbal ability (X) and abstract reasoning (Y) are represented in the following table:

Y/X 20 30 40 50
(25-35) 6 4 0 0
(35-45) 3 6 1 0
(45-55) 0 2 5 3
(55-65) 0 1 2 7

1 Is there a correlation between the two variables?

2 According to the data, if one of these students obtained a score of 70 points in abstract reasoning, what would be the estimated score in verbal ability?


Turn the double entry table into a single table.

xi yi fi xi · fi xi2 · fi yi · fi yi2 · fi xi · yi · fi
20 30 6 120 2,400 180 5,400 3,600
20 40 3 60 1,200 120 4,800 2,400
30 30 4 120 3,600 120 3,600 3,600
30 40 6 180 5,400 240 9,600 7,200
30 50 2 60 1,800 100 5,000 3,000
30 60 1 30 900 60 3,600 1,800
40 40 1 40 1,600 40 1,600 1,600
40 50 5 200 8,000 250 12,500 10,000
40 60 2 80 3,200 120 7,200 4,800
50 50 3 150 7,500 150 7,500 7,500
50 60 7 350 17,500 420 25,200 21,000
    40 1,390 53,100 1,080 86,000 66,500

Correlation and Regression Calculations

Correlation and Regression Calculations

Correlation and Regression Calculations

Correlation and Regression Calculations

Correlation and Regression Calculations

Correlation and Regression Solution

Correlation and Regression Solution