(c) for subsample 12 leter a test two subsam Conduct data into model to Divide t

Question

(c) for subsample 12 leter a test two subsam Conduct data into model to Divide the the and r 12, d fit (a) the equation breakdowns durin temperature of the and if is only (d) on your results from parts b and c, how on the assembly li (b) A 95% prediction should the estate proceed? of 8.13 Assembly line breakdowns. Breakdowns machines that produce steel are very costly. the fewer 0, For those same va and the smaller the company's profits. To help profit loss, the of a can company like a model that will predict the ables, find a 95% number of break (c) A 95% confiden X1 0,x2. 0, x3 number of breakdowns on the assembly line The proposed by the company's statisticians is the following: 2.107). Using onl problem, is it pos 8.15 Purchasing a service where y is the number of breakdowns per 8-hour retail appliance stor shift, tion of appliance ov 1 if midnight a service contract f 1 if afternoon shift shift Since the manager x1 0 otherwise 0 otherwise decreases with age x is the temperature of the plant (F, and he will fit the first-o is the number of inexperienced personnel working on the assembly line. After the model is fit using the least squares procedure, the residuals are plotted A sample of 50 against i, as shown in the accompanying figure. are contacted abo ing a service cont machines and 50 or (y y) old machines are another survey is The proportion y the service policy S APPLIANCE Age of Appliance x, years Proportion Buying Service Contract. y (a) Fit the first-o (b) Calculate the plot versus (a) Do you detect a pattern in the residual plot? (c) What does What does this suggest about the least squares the varia assumptions? (d) Explain

Explanation / Answer

a)One of the most important assumption of the least square estimate is that the error variances are constant.Here from the above figure we can see that that the deviation of error from the x-axis is not constant.In other words,it violates the assumption of homoscedasticity.The shape of the residual is funnel shaped according to the above figure and it violates one of the important assumption of homoscedasticity.

b)If the error or the residual of the above distribution was constant then the distribution would have been norma.However the error depends on the y.Thus the variance of Y are a function of mean.Taking higher power of x or square root of the variables can be considered so as to take into account the error variances.This would make our model more realistic.One possible solution would be to take the square root of Y and then use multiple regression instead of Y.

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