Question

Case: A small convenience store chain is interested in modeling the weekly sales of a store, y, as a function of the weekly traffic flow on the street where the store is located. The table below contains data collected from 24 stores in the chain.

Store	Weekly Traffic Flow (thousands of cars)	Weekly Sales ($ thousands)
1	59.3	6.3
2	60.3	6.6
3	82.1	7.6
4	32.3	3.0
5	98	9.5
6	54.1	5.9
7	54.4	6.1
8	51.3	5.0
9	36.7	3.6
10	23.6	2.8
11	57.6	6.7
12	44.6	5.2
13	75.8	8.2
14	48.3	5
15	41.4	3.9
16	52.5	5.4
17	41.0	4.1
18	29.6	3.1
19	49.5	5.4
20	73.1	8.4
21	81.3	9.5
22	72.4	8.7
23	88.4	10.6
24	23.2	3.3

1) Present the weekly sales vs. traffic flow scatter plot using MS Excel. Clearly label the graph elements (horizontal and vertical axes, and overall title).

Scatter plot [2marks]:

The following questions are based on ‘y = β₀ + β₁x +e’, the linear regression model, where y is the weekly sales and x is the traffic flow. You will be estimating this model using the Least Squares method to give the prediction equation: y=b0+b1x.

2) What value have you found for b₀?

b₀ = ____________________ [1 mark]

3) What value have you found for b₁?

b₁ = ____________________ [1 mark]

4) Write down the fitted (prediction) equation:

________________________________________ [1 mark]

5) What is the coefficient of determination (R²) for this regression model?

R²: ____________________ [1 mark]

6) The chain wants to establish a new store at a location where the weekly traffic flow is 50.4 thousand cars. Use the fitted equation to predict the weekly sales of the planned store:

____________________________________________________________ [1 mark]

Test the null hypothesis that b₁ = 0 against the alternative that b₁ ¹ 0. The significance level to be used is 5%.

7) What are the critical values for the test?

____________________ [2 marks]

8) Write down the value you have found for the test statistic:

____________________ [1 mark]

9) State your decision (Reject or Do not Reject the Null Hypothesis?):

____________________________________________________________ [1 mark]

10) In one sentence, what does the outcome of this hypothesis test allow you to conclude about the relationship between weekly sales and weekly traffic flow?

____________________________________________________________________________________________________

________________________________________________________________________________ [2

Answer 1