problemis to be complete dusingthe MI Problem 3 Using the OUIPULA3 provided (see
ID: 3217382 • Letter: P
Question
problemis to be complete dusingthe MI Problem 3 Using the OUIPULA3 provided (see output at the end of this packet), answer the following questions. NOTE: the model is using a business's Assets variable (in millions) to predict their Sales (in Millions) LNCLUDEIHEUMPOUIPULwhichwas given to you in your solution packet aswelLafter your problem 3 solution. Only answer what is asked, please. a) Comment on the Correlation observed between the independent variable and the response variable and note which plot/output was used for this solution. Is simple linear regression appropriate model, why or why not? b) What is the current predictive regression equation (in context of the variable names in appropriate format)? c) Complete/Calculate the values for ALL the missing cells in OUTPUT3 for the Anova table section. (do NOTwrite them on the output, but in your solutions in ORDER, labeled as partcetc., and make it easy to read and understand all your work and label what you are calculating). Note: some of the sum of squares are in scientific notation format and you are NOT to answer in scientific notation but answers in tegular decimal format not scientific notation. d) Notice that the root mean square error is blank. Calculate it. (using output shown & show allwork.) e) What is the proper interpretation of the slope? f) How many observations were used to create this predictive equation? g) What is the appropriate test statistic and pvalue for the Test of slope for this model/output (show full work for the test statistics and full calculator syntax for the pvalue.) h) BONUS: Calculate the residual for the first observation from the dataset First observation: Asset ($Mil): 7919 with Sales($Mil): 9844Explanation / Answer
(a) As, Rsq = 0.94, the correlation between the independent and response variable is high. This can also seen in the first plot (Sales vs Assets) where the relation between Sales and Assets is linear and showing positive correlation.
Yes, simple linear regression is appropriate for this model because the linear model (lm) assumption does hold for this model.
- Residuals by predicted plot have no detectable patterns, so residuals (errors) have constant variance.
- Residuals Normal Quantile plot does display a linear pattern, so residuals (errors) are normally distributed.
Also Rsq is large for the model, so simple linear regression is appropriate for this model.
(b) Sales = 648.42652 + 0.9523774 * Assets
(c) SST = SSM + SSE
1.5621e+10 = 1.4724e+10 + SSE
SSE = 1.5621e+10 - 1.4724e+10 = 897000000
Mean square for Total = SST/ df = 1.5621e+10/94 = 166180851
Df for model = SSM/ Mean error for model = 1.4724e+10/1.472e+10 = 1
Df for error = SSE/ Mean error for error = 897000000/9649141.6 = 93
(d) MSE = 9649141.6
RMSE = sqrt(9649141.6) = 3106.307
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