a) State the unique issue(s) relevant to a multiple linear regression, with focu

Question

a) State the unique issue(s) relevant to a multiple linear regression, with focus on the correlation of independent variables and the interpretation of their effects. b) A random sample of 30 individuals is collected on their smoking habits. The sample contains the information on: y = The number of packs of cigarettes consumed per month x_1 = Age of a smoker x_2 = Annual income x_3 =Typical price per pack of cigarette The correlation matrix for these variables is given by Table Q4(b): Discuss and analyze the basic interrelationships suggested by the above information The following two regressions are conducted: y_i = 28.60 + 0.258x_2j - 11.39x_3j (1.53) (10.82) (1.30) R^2 = 0.83 and y_j = -11.74 + 0.986x_1j + 0.084x_2j - 0.531x_3j (0.78) (5.38) (2.30) (0.08) R^2 = 0.91 Figures in brackets are the t-values for individual parameter estimates. Discuss and interpret the two regressions in the light of the correlation matrix given.

Explanation / Answer

(i)

there are positive correlation between y and x1 , y and x2

there is negative correlation between y and x3

there are negative correlation between x1 and x3 , x1 and x2

there is positive correlation between x1 and x2

positive correlation means if one variable increases others will also increase and vice-versa

negative correlation means if one variable increases others will decrease and vice-versa

(ii) let beta1 is coefficient of x1, beta2 is of x2 and beta3 is of x3 and beta0 is constant

in both the model only beta3 are significant as absolute t-value is more than t-critical at 5% level of significance.

in the first model we can remove the variable x2

In model 2, inclusion of variable x1 does not give impact as it is not significant.

so only one variable x3 is significant from both the model.

model1 coefficeint SE t t-critical beta0 28.6 1.53 18.69281 2.05183 (t(0.05,27) beta2 0.258 10.82 0.023845 beta3 -11.39 1.32 -8.62879 model2 coefficeint SE t t-critical beta0 -11.74 0.78 -15.0513 2.055529 (t(0.05,26) beta1 0.986 5.38 0.183271 beta2 0.084 2.3 0.036522 beta3 -0.531 0.08 -6.6375

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