MINITAB was used to fit the model Y = beta_0 + beta_1 x_1 + beta_2 x_2 + beta_3

Question

MINITAB was used to fit the model Y = beta_0 + beta_1 x_1 + beta_2 x_2 + beta_3 x_3 + beat_4 x_4 + epsilon to n = 12 data points. A portion of the output is given below. Analysis of Variance Model Summary S R - sq R - sq (adj) ? 71.93% 55.89% Coefficients Regression Equation Y = -34 + 1.011 x1 + 4.85 x2 + 1.76 x3 - 0.253 x4 a) Fill in the missing values. (Write approximate values of P - values) b) Is the model overall significant at alpha = 0.05? c) Is x4 a significant variable for the model? d) Estimate true beta_1 with a 98% confidence interval. e) What is the proportion of variability in response explained by this regression model?

Explanation / Answer

we know that MS = SS / df

so 4728.05/4 = 1182.01

t value = coeff/ SE = 1.011/0.370 = 2.732

c)

no we see that the p value of x4 is 0.787 , which is not less than 0.05 , hence we can conclude that the variable x4 is not significant at this level of significance

d) we see that b1 = 1.011 and SE coeffiecint is 0.370 from the regression output table.

also , from the z table we know that for 98% CI the value of z is 2.33

so using the equation

estimate +- z*SE we get

1.011 +- 2.33*0.370 , solving this for + and - we get the range as

0.1489 , 1.8731

e) we see that the r2 value is 71.93% , so this means that the model is able to explain 71.93% variation of the data

please note that we can answer onyl 4 subparts of a question at a time , as per the answering guidelines

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