uestion 3 A hypothetical mobile phone company operates tw0 burently sells Abelow

Question

uestion 3 A hypothetical mobile phone company operates tw0 burently sells Abelow in own for products. A researcher estimated a population an es in a big city and a small selling its phone products. The company currently atyse the factors that affect the profitability of the company sells 40 different p model as shown below in orde y ist anual earnings per share (in dollar) of the company co odts, X1 and x2 are the sale number of mobile phones, an 40 products (simplified as the difference between product price an contributed by the the profit margin of the to one if the cost of a phone set), respectively. Xs is a dummy variable which is equa branch location is in the big city, x3 is zero if the branch location is in the sma ocatich isand he sample regression equation results are given below: y = 0167 + 0.1 73x; + 0.365X2 + 0.073x3 + residual, (0.049) (0.086) (0.117) (0.006) The figures in parentheses below the coefficient estimates are estimated standard a) Explain the economic meanings of the coefficient estimates for 1 and 2- R2 = 0.91 errors [10%) b) Given the coefficient estimates and standard errors (in parentheses): i) Set up a test for the null hypothesis that 2 is zero or negative against a [20%) ii) Perform the test for the hypothesis and explain your conclusion from the test. suitable alternative hypothesis with a significance level of 1%. [20%) c) Given the coefficient estimates and standard errors (in parentheses) i) Set up a test for the null hypothesis that is zero or negative against a suitable alternative hypothesis with a significance level of 1%. [20%) i) Perform the test for the hypothesis and explain your conclusion from the test. [20%) d) From your test results above in c) interpret the meaning of

Explanation / Answer

Part a

The coefficient estimates for 1 is given as 0.173 and coefficient estimate for 2 is given as 0.365. The estimate for 1 suggests the 0.173 increment in the dependent variable y as per unit increase in independent variable or explanatory variable X1. The estimate for 2 suggests 0.365 increments in the dependent variable y as per unit increase in independent variable or explanatory variable X2.

Part b.i.

We have to use t test for regression coefficients. Null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: 2 0

Alternative hypothesis: Ha: 2 > 0

This is a one tailed test. This is an upper tailed or right tailed test.

Part b.ii.

We are given

= 0.01

n = 40

df = n – 1 = 40 – 1 = 39

2­­_hat = 0.365

SE(2­­_hat) = 0.117

Test statistic = t = 2­­_hat / SE(2­­_hat) = 0.365 / 0.117 = 3.11965812

P-value = 0.001699

P-value < = 0.01

So, we reject the null hypothesis that 2 0.

There is sufficient evidence to conclude that 2 is greater than zero.

Part c.i.

Null hypothesis: H0: 3 0

Alternative hypothesis: Ha: 3 > 0

This is a one tailed test. This is an upper tailed or right tailed test.

Part c.ii.

We are given

= 0.01

n = 40

df = n – 1 = 40 – 1 = 39

3­­_hat = 0.073

SE(3­­_hat) = 0.006

Test statistic = t = 3­­_hat / SE(3­­_hat) = 0.073/0.006 = 12.16667

P-value = 0.00

P-value < = 0.01

So, we reject the null hypothesis that 3 0.

There is sufficient evidence to conclude that 3 is greater than zero.

Part d

From above part c, it is observed that the coefficient 3 is statistically significant and we can use the independent variable X3 in the given regression model as the coefficient of this variable is found statistically significant and useful.

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