Question

Consider the following data on x and y shown in the table below,

x	2	4	7	10	12	15	18	20	21	25
y	5	10	12	22	25	27	39	50	47	65

Fit the model E(y)=β0+β1x to the data, and plot the residuals versus x for the model on Minitab. Do you detect any trends? If so, what does the pattern suggest about the model?

Answer 1

a) The step-by-step instructions to obtain simple linear regression output using Minitab 18: *Store the variables (X) and (Y) in the columns of the Minitab 18 worksheet Choose the Regression -Regression ->Fit Regression model * Select the variable (Y) in the Responses box and then select the variable (X) in the Continuous Predictors box. * Click ok. The simple linear regression output

Regression Analysis: y versus x Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 1 3303.5 3303.54 191.43 0.000 1 3303.5 3303.54 19143 0.000 8 8 17.26 9 3441.6 Error Total Model Summary S R-sq R-sq(adj) R-sq(pred) 4.15417 95.99% 95.49% 93.16% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant -3.182.75-1.16 0.281 2.491 0.180 13.84 0.000 1.00 Regression Equation y 3.18 + 2.491 x

The least-squares regression line of the simple linear regression equation is -3.18+2.491X Y-I-318+2.491x

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(b) The step-by-step instructions to obtain simple linear regression output using Minitab 18: *Store the variables (X) and (Y) in the columns of the Minitab 18 worksheet * . Choose the Regression -Regression ->Fit Regression model * Select the variable (V) in the Responses box and then select the variable (X) in the Continuous Predictors box. * Click Graphs → Residuals for plots → Regular → Residuals versus X. * Click ok. The simple linear regression output:

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Residuals from y vs x Residuals Versus x (response is y) 5.0 2.5 E 0.0 2.5 5.0 7.5 0 10 15 20 25

Interpretation:

The plot of the residuals versus the independent variable (X) for the model explains the linear relationship between the variables. There is no existence of non-linear pattern in the plot and there is no evidence of unequal variances in the data. The pattern is linear and it explains 95.99 of the variation in the dependent variable (Y) can be explained by the independent variable (X) of the model. The model is a very good fit for the given data.