STA104 WEEK 8

Video V1W8: Prediction Using Estimated Linear Regression 

LEARNING OBJECTIVE 2

Coefficient of Determination (R-Square)

Students need to know how to calculate and interpret the meaning of coefficient of determination, R2.

👉🏼 Refer Pg. 81 (formula)

👉🏼 Watch Video V2W8 

👉🏼 Redo Example 4(e) Pg. 82

Please do the following exercises for better understanding on this topic:

EXAMPLE 5 (Pg.83)

Answer:

a) X: Annual income       Y: Monthly insurance

b) r = 0.891 (There is a strong positive correlation between annual income and monthly insurance)

c) R2 = 79.39%

d) y = -147.4745 + 6.3074x

e) Slope, b = 6.3074 indicates that for every thousand increase in annual income of a personnel, their monthly insurance premiums will increase by RM6.31.

*In this example, it is not suitable to interpret value a (y-intercept)

f) RM 546.34

EXAMPLE 6 (Pg. 84)

Answer:

a) X: Batch Size        Y: Direct labor cost

b) r = 0.9996 (There is a very strong positive correlation between batch size and direct labor cost)

c) y = 18.5295 + 10.1545x

Slope, (b) = 10.1545 indicates that for additional unit of batch size, direct labor cost will increase by RM10.15.

d) RM 983.21

e) R2 = 99.92%

EXAMPLE 7 (Pg. 85)

Answer:

a) X: Amount of fertilizer       Y: Units of fruits

b) r = 0.8271 (There is a very strong positive correlation between amount of fertilizer and units of fruits produced)

c) R2 = 68.41% indicates that 68.41% of total variation in units of fruits produced can be explained by amount of fertilizer used.

d) y = 12.2814 + 0.5683x

e) y-intercept (a) = 12.2814 indicates that when fertilizer is not applied to the plants, units of fruits produced will increased by 12.2814 units (approximately 12 units).

Slope, (b) = 0.5683 indicates that for every gram increased in amount of fertilizer used, units of fruits produced will increased by 0.5683 units. (approximately 1 unit)

f) 0.2kg x 1000 = 200g

   y = 12.2814 + 0.5683(200)

   y = 125.9414

   y = 126