Question

 

Fill in the empty cells in the following table in order to calculate the standard error of the estimate. 

X	Y
3	3	6.00	-3.00	9.00
6	9	7.50	1.50	2.25
5	8	7.00	1.00	1.00
4	3	6.50	3.50	12.25
7	10	8.00	2.00	4.00
5	9	7.00	2.00	4.00
---------------	---------------	---------------	---------------	Sum = 32.5

Note: Sum in the last column is , which is SS_residual.

F. Use the formula and information on p.15 of the Week 12_3 slides. What is the value of the standard error of estimate?What is the value of the residual variance or error variance (MS_residual)? (2 decimals)  

= 2.85

MS_residual = 8.13

G. Use the correlation coefficient you have calculated and p.16 of the Week 12_3 slides. Calculate the coefficient of determination (r²) and interpret its meaning in one sentence. [2 marks]

r² = 0.800

. Fill in the empty cells in the following table in order to calculate the standard error of the estimate. 

X	Y
3	3	6.00	-3.00	9.00
6	9	7.50	1.50	2.25
5	8	7.00	1.00	1.00
4	3	6.50	3.50	12.25
7	10	8.00	2.00	4.00
5	9	7.00	2.00	4.00
---------------	---------------	---------------	---------------	Sum = 32.5

Note: Sum in the last column is , which is SS_residual.

F. Use the formula and information on p.15 of the Week 12_3 slides. What is the value of the standard error of estimate?What is the value of the residual variance or error variance (MS_residual)? (2 decimals) 

= 2.85

MS_residual = 8.13

G. Use the correlation coefficient you have calculated and p.16 of the Week 12_3 slides. Calculate the coefficient of determination (r²) and interpret its meaning in one sentence.  

r² = 0.800

Answer 1

X	Y	Fitted value (Y^)	Residual (e)=Y-Y^	Residual square=e^2
3	3	6	-3	9
6	9	7.5	1.5	2.25
5	8	7	1	1
4	3	6.5	3.5	12.25
7	10	8	2	4
5	9	7	2	4
30	42	42	7	32.5

F. Use the formula and information on p.15 of the Week 12_3 slides. What is the value of the standard error of estimate? What is the value of the residual variance or error variance (MSresidual)? (2 decimals) [2 marks]

Ans:

Standard error of estimate=sqrt(SSresidual/(6-2))= sqrt(32.5/4)= 2.85

Residual variance= SSresidual/(6-2)= 32.5/4=MSresidual = 8.13

G. Use the correlation coefficient you have calculated and p.16 of the Week 12_3 slides. Calculate the coefficient of determination (r2) and interpret its meaning in one sentence. [2 marks]

r2 = 0.800

ANS;

Interpretation: 80.00% variation of the total variable of Y is explained by the explanatory variable X.