Question

Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales ($ thousands) last month for each client sampled.

Number of Contacts (X)	Sales ($ thousands) (Y)
14	24
12	14
20	28
16	30
46	80
23	30
48	90
50	85
55	120
50	110

1. Determine the standard error of estimate
2. Determine the coefficient of determination. Interpret the coefficient of determination

Answer 1

	X	Y	X * Y	X2	Y2
	14	24	336	196	576
	12	14	168	144	196
	20	28	560	400	784
	16	30	480	256	900
	46	80	3680	2116	6400
	23	30	690	529	900
	48	90	4320	2304	8100
	50	85	4250	2500	7225
	55	120	6600	3025	14400
	50	110	5500	2500	12100
Total	334	611	26584	13970	51581

Part a)

Y	Ŷ
24	18.52395	29.98714259
14	14.13466	0.01813455
28	31.6918	13.6293822
30	22.91323	50.22228139
80	88.75249	76.60603234
30	38.27572	68.48762169
90	93.14177	9.870724341
85	97.53105	157.0273288
120	108.5043	132.1519511
110	97.53105	155.4746
611	611	693.475199

Standard Error of Estimate S = √ ( Σ (Y - Ŷ ) / n - 2) = √(693.4752 / 8) = 9.3104

Part b)

r = 0.975

Coefficient of Determination
R² = r² = 0.951

Interpretation

R² implies the percentage of variation explain in dependent variable by independent variable.

Explained variation = 0.951* 100 = 95.1%