Question

The following data pertain to the amount of hydrogen present, y, in parts per million in core drillings made at 1-foot intervals along the length of a vacuum-cast ingot, x, core location in feet from base:

x 1 2 3 4 5 6 7 8 9 10

y 1.28 1.53 1.03 0.81 0.74 0.65 0.87 0.81 1.10 1.03

1.Check the assumptions for this model

2.Find R-square adjusted and provide and interpretation of this value

Answer 1

Result:

The following data pertain to the amount of hydrogen present, y, in parts per million in core drillings made at 1-foot intervals along the length of a vacuum-cast ingot, x, core location in feet from base:

x 1 2 3 4 5 6 7 8 9 10

y 1.28 1.53 1.03 0.81 0.74 0.65 0.87 0.81 1.10 1.03

1.Check the assumptions for this model

Residual plot.

The plots shows that the assumptions are met.

2.Find R-square adjusted and provide and interpretation of this value

R square = 0.1838 or 18.38%

R square adjusted = 0.0818 or 8.18%

8.18% of the variance in y is explained by x.

MINITAB used.

Regression Analysis: y versus x

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	1	0.1191	0.11913	1.80	0.216
x	1	0.1191	0.11913	1.80	0.216
Error	8	0.5289	0.06612
Total	9	0.6481

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
0.257128	18.38%	8.18%	0.00%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	1.194	0.176	6.80	0.000
x	-0.0380	0.0283	-1.34	0.216	1.00

Regression Equation

y

=

1.194 - 0.0380 x