? canvas.cwu.edu r information-Born Primitive answer (that is, what about the gr

Question

? canvas.cwu.edu r information-Born Primitive answer (that is, what about the graph makes you answer that way). 10 points per graph ( pt. per answer a-e, and 1 pt. for explaining each answer). a) Does there appear to be a positive, negative, or no relationship? How can you tell? b) Is there any evidence of a non-linear relationship? Why or why not, and what effeet will this have on the correlation coefficient (in other words, why does this matter)? c) Is there any evidence of issues such as heteroscedasticity or outliers? Why or why not, and what effect will they likely have if they're there? d) Roughly, what range would you expect r to be in? Why? (You should explain what r' is on at least your first answer). e) Given all of your answers above, how accurate would you expect to be in predicting future Y scores based on X (i.e., would you expect the Standard Error of Estimation to be high, low, or moderate)? If you have said that there is no relationship, what would the Standard Error of Estimation be equal to (don't need to calculate a value here - recall that there is an upper limit to the SEoE)

Explanation / Answer

a)

There appears to be a negative relationship between the two variables. From the scatterplot, as the age increases the Value of Car decreases. (if we draw a linear line, the slope of this line would be negative)

b)

Yes, the non-linear relationship seems to be present between the two variables. The curved pattern in the scatter plot indicates that the rate of increase or decrease can change as one variable changes. Hence, non-linear relationship seems to be present between the two variables

Correlation coefficient is a measure of strength of linear relationship between the variable. It may provide false results for non-linear relationship.

c)

There are no outliers but heteroskedasticity seems to be present. (Absence of constant variance between Error Terms leads to heteroskedasticity. Since the data is non-linear, the will not be constant variance in the Error Terms.)

Presence of heteroskedasticity can lead to invalidation of statistical tests of significance that assume that the modelling errors are uncorrelated and uniform.

d)

R square should be in the range of 0.6 to 0.9 for a linear model. Since there seems to be a moderately strong negative relationship between the two variables and the range of R Square is generally 0.6 to 0.9 for such cases.

e)

The Standard Error of Estimate would be high since there is negative non-linear correlation between the two variables.

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