Question

The following information regarding a dependent variable (Y in $1000) and an independent variable (X) is provided.

Σ(x,- x)(y-y) = - 12 ΣΧ= 16 ΣΥ,-y)2 = 18 Σ(x,- x) = 8

Y Dependent Variable

15

17

23

17

I. The least-squares estimate of the slope equals:

II. The least-squares estimate of the intercept equals:

III. If the independent variable increases by 2 units, the dependent variable is expected to

a. decrease by $300

b. decrease by $3000

c. decrease by $3

d. decrease by $2

e. none of the above

     The letter corresponding to the answer is: .

IV. The sample correlation coefficient equals:

V. The coefficient of determination equals:

VI. What can we say about the linear association between X and Y?

a. There is a perfect positive linear relationship between the two variables.

b. There is a strong positive linear relationship between the two variables.

c. There is a strong negative linear relationship between the two variables.

d. There is a moderate positive linear relationship between the two variables.

The letter corresponding to the answer is: .

Answer 1

OLS &q= sxy =4 estimate sxx {(xi-x)(4:4) Elxi-x) - 12 8 11 3 .-1.5 2 of 7 - Bix 5+17 +23+17) -(-15) ΣΧ 4 0 +1.5X 16 24

St. No cello Title 1. Page No Sports least square estimate of slops equal -1.9 square estimate of intercept equals 24 The estimated regression equation - प - $ + X 24 1.5X of the independent variable is incresed by 2 unita then (x₃x+2) 24 -1.5(x+2) 24 -1.5X1.5X2 ŷ - 3 dependent variable expected to decrease by $3. option c is correct ans wer. The letter forresponding to answer is C. The correlation caufficient equals sexy ( -12) 8 x 18 IV. sample R2 = sxx syt The sample correlation couldicient infrat

v) The calfficient of determination equal as (R² = 1) from previous part. 1 1 2 3 5 VI) since R?=1 There is berfect bositive linear relation ship between the two variables 10 12 The to the le ter answer corresponding is a 19 20