Question

Mr. James, president of Daniel-James Financial Services, believes that there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, he gathered the following information from a sample of clients for the last month. Let X represent the number of times that the client was contacted and Y represent the value of sales ($1000) for each client sampled. Number of` Sales Contacts

(X) ($1000) (Y)

14    24

12 14

20 28

16 30

23 30

a) Compute the regression equation for client contacts and sales. Interpret the slope and intercept parameters.

b) Compute the correlation coefficient and coefficient of determination. Interpret the coefficients.

c) James would like to require 30 client contacts per month. Based upon the above data, predict what the monthly sales would be for this number of client contacts. What would be your advice to Mr. James about his proposed policy?

Answer 1

X Y XY X^2 Y 2 14 24 196 576 336 12 14 144 196 168 20 28 400 784 560 16 30 256 900 480 23 30 529 900 690 SUM= 85 126 1525 3356 2234

Ans ta) Reg»esson Equation abx EX = 85, LY= 12 6, 2x2= 15 2 5, £y2= 336, £xy: 2234, Σχ2 ΣΥ-Σχ Σχy li52Sx 126)- (asx 2234) (5x 1525)-(05)2 n x2 (Zx) 2 22 6o 5 65 4 0o (sx 2234)- O5 X126) η ΣΧΥ- ΣΧ ΣΥ (5X152 5)-(S ηΣΧΣ-(Σx). 46 0 4uo b- .15 5. 6 5 5 X Interpretotion of opeInteropt have the we get Y- fnfe rcapt ohich igual to the intercapt the line zero conta et the dale willb Hen a for 5.6 S thich' i constond.

COYTE lation (oefficient ne 5 A3 x3 - h X7 u -h Exx2nY-Y Zxy : 2234 (Sx 2234) (8sx 126) 525S 35-24 (5x3 46 0 60.3319 Y 07649 69 Y= 0.7 65 Coctficient determinatian Y b6496gj7 505177 Interpre totion o Y The cocffi cient j (orvelation gîvea the correlation bet ween data Hen c number positi vely Correlatıd. ib a meapuire oi how'much ot variab?lity variable con beex p lained byvariationin the Contacts ancd sales a re Gther in ane voriable cOn be explained by 59 vorio blitcb variotion fn the other Here

17 IS * 30 S-6 S y 40. 3 - 40.1S Contocts Monthly Aales tor 30 It Jomes Contac t th en saleo a ocreaAe abo fncreases