Question

Two nonprofits are interested in sharing fundraising lists and campaigns as they think their donors share common interests. Implicit in that assumption is they are related variables. You collect data below for thirteen donors and want to test if there is a relationship between donations (in dollars) (data is collected below)

Charity A:  

50 70 60 30 30 60 100 20 40 60 30 80 60

Charity B:

60 45 65 50 30 30 90 40 50 70 40 55 40

a.) State the null both formally and in lay terms
b) Calculate r and the regression line (y = a + bx) and reject/accept at a=.05. What is the regression line please state it?

c) Explain your findings in lay terms using r-square, r, b as appropriate

d) Calculate a 95% confidence interval for the slope if it is necessary if it is not please explain. Provide the formal interval and explain in layterms.

Answer 1

For the given data------

a) null hypothesis: There is no relationship between donations of charity A and charity B

Alternative hypothesis: There is an  relationship between donations of charity A and charity B

b) I have used minitab to find regression line------

Steps---

Enter the data in minitab---click<stat----click<regression---click<regression---

The output of minitab is----

The fitted regression line is----

Decision about Rejection or acceptance-----

For Testing the slope coefficient b,

Hypothesis is given by----

p- value= 0.02<0.05 so we reject the null hypothesis H₀

Regression Equation y = 26.18 +0471 Coefficients Term Coef SE Coef T-Value Constant 26.18 9 .94 2.63 0.471 0.173 2.72 VIF P-value 0.023 0.020 1.00 Model Summary S R-sq R-sq(adj) R-sq(pred) 13.7101 40.20% 34.77% 10.50%

y = 26.18+ 0.471 * I

R = 0.402

T= V0.402 = 0.634

H:b=0

H.: 670