a- There is no striking evidence in the plot that the assumptions for regression

Question

a- There is no striking evidence in the plot that the assumptions for regression are violated and there is a clear straight line trend.

b-There are very influential observations in the plot suggesting that our results must be interpreted with extreme caution.

c-The plot contains many fewer points than were used to fit the least-squares regression line in the previous problems. Obviously there is a major error present.

d-The plot contains dramatic evidence that the standard deviation of the response about the true regression line is not even approximately the same everywhere.

A random sample of 79 companies from the Forbes 500 list (which actually consists of nearly 800 companies) was selected, and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. The following simple linear regression model was used

Profitsi = 0 + 1(Sales)i + i

where the deviations i were assumed to be independent and Normally distributed, with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software:

R2 = 0.662
s = 466.2 Variable Parameter Estimate S.E. of Parameter Estimate Constant –176.644 61.16 Sales 0.092498 0.0075 Reference: Ref 10-3
A scatterplot of sales versus profits is given below.



Which of the following statements is supported by the plot?

Explanation / Answer

Scatter plots are similar to line graphs in that they use horizontal and vertical axes to plot data points. However, they have a very specific purpose. Scatter plots show how much one variable is affected by another. The relationship between two variables is called their correlation .

b-There are very influential observations in the plot suggesting that our results must be interpreted with extreme caution.

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