Question

This question presents regression output from a model predicting life expectancy from gross national product. The model output is also provided below: Variable Estimate Standard Error T Value Pr (> |t| ) Intercept 69.4 0.54 126.7 0.000 Gross National Product 0.000323 0.00004 8.06 0.000 (a) Write out the regression equation (b) Interpret the coefficient and the slope (c) What are the hypotheses for evaluating if gross national product has any impact on life expectancy? (d) State the conclusion of the hypothesis test from part (c) in context of the data. (e) If the R2 is 34%, what is the correlation? Interpret R-squared in the context.

Answer 1

Solution:

a) The estimated or fitted least square regression equation for predicting life expectancy is

​​​​​​

Where y = life expectancy

And X = Gross national product.

b) Interpretation of intercept .

When X= 0 then is the mean of life expectancy (y). when X not equal to zero then intercept has not physical interpretation.

Interpretation of slope

When one unit in gross national product increases then the average life expectancy increases by 0.000323

OR

When one unit change in gross national product (X) then the average or mean change in life expectancy (y).

c) Test for significant of gross national product.

To test the hypothesis

. Vs.

Test statistic

t = 8.06

P Value = 0.0000 given

At level of significance

P value

Rejecte Ho

d) conclusion: There is linear relationship between Life expectancy and gross national product.

Gross national product is significant to the model.

Gross national product impact on the life expectancy.

e) The value of the coefficient of determination

Interpretation : The response variable life expectancy explain 34% of the variability in the model due to predictor variable gross national product.

In short 34 % of the model is good fit.

The value of the then the value of the correlation coefficient r = 0.583