Question

The following table contains results from the regression of sales price (y) on lot size (x₁), number of bedrooms (x₂), number of bathrooms(x₃) and number of storeys (x₄). Sales price is the dependent variable and x₁,x₂,x₃,x₄ are independent variables.

R² = 0.54

F= stat = 48.3235

p value and F - stat of 1.18E - 88

n > 30.

a. Write down the least square prediction equation

b.use R² to check the validity of the model.

c use " t-stat" to check the validity of the coefficient at 5 % sig. level

d.use P value to check the validity of the coefficient at 1% sig level

e verbally explain each coefficient

f. check the validity of the model at 5% sig level ( use F stat and its P value )

Answer 1

a. The least square prediction equation for y using the 4 predictors can be expressed as:

b. The coefficient of determination R² = 0.54.It implies that the 4 predictors together explains about 54% variation in y. It suggests a moderately efficient fit to the data.

c. The t-statistic for testing the significance of the slope corresponding to each of the 4 each of the 4 predictors tests the hypothesis:

Vs

If the test statistic t exceeds the critical value, ( |t| > t), we may reject H₀ at % level of significance.We may then conclude that 'i' is significant in predicting the response 'y'.

d. If the p-value of the slope coefficient for the predictor is less than the significance level, we may reject H₀ at % level of significance.

e. The coefficient of determination is a measure to validate the model and test its goodness of fit to the data.It gives the amount of variation in y that is explained by the predictors of the model.It ranges from 0 to 1.The higher the R², the better the model)

The t test statistic and the p- value are the measures using which conclusions are drawn as to whether the coefficient or the test is significant or not.

f. Comparing the F statistic with the critical value, obtained from F table, and looking at the p value 0.000<0.05, we may conclude that the model is significant at 5% level.

It may be inferred that the predictors contribute significantly towards explaining the response variable through this linear model.