Question

The statements in this question are based on the following data: X 2:6 2:6 3:2 3:0 2:4 3:7 3:7 PX D 21:2 Y 5:6 5:1 5:4 5:0 4:0 5:0 5:2 PY D 35:3The correlation coefficient .r/ was calculated as 0:327: Identify the incorrect statement.
1. There is a positive relationship between x and y. 2. N y D 5:043 3. The coefficient of determination is 0:5719:
4. The regression coefficient b1 is also positive.
5. Only 10.7% of the variation in y is explained by the variation in x:

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
2.6	5.6	0.18	0.31	-0.24
2.6	5.1	0.18	0.00	-0.02
3.2	5.4	0.03	0.13	0.06
3	5	0.00	0.00	0.00
2.4	4	0.40	1.09	0.66
3.7	5	0.45	0.00	-0.03
3.7	5.2	0.45	0.02	0.11

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	21.2	35.3	1.694285714	1.6	0.53
mean	3.03	5.04	SSxx	SSyy	SSxy

sample size ,   n =   7          
here, x̅ = Σx / n=   3.03   ,     ȳ = Σy/n =   5.04  
                  
SSxx =    Σ(x-x̅)² =    1.6943          
SSxy=   Σ(x-x̅)(y-ȳ) =   0.5          
                  
estimated slope , ß1 = SSxy/SSxx =   0.5   /   1.694   =   0.3137
                  
intercept,   ß0 = y̅-ß1* x̄ =   4.0929          
                  
so, regression line is   Ŷ =   4.0929   +   0.3137   *x

1) There is a positive relationship between x and y

Since r = 0.327 is positive , relatioship is positive

TRUE

2)

2. N y D 5:043

ȳ = Σy/n =   5.043

TRUE

3. The coefficient of determination is 0.5719

r = 0.327

R2 = 0.1070

FALSE

4. The regression coefficient b1 is also positive.

Ŷ =   4.0929   +   0.3137   *x

TRUE

5. Only 10.7% of the variation in y is explained by the variation in x:

R2 = 0.1070 = 10.7%

TRUE

Please revert in case of any doubt.

Please upvote. Thanks in advance