Question

In: Statistics and Probability

Scenario: The researhers want to know if there is a relationship between the number of cars...

Scenario:
The researhers want to know if there is a relationship between the number of
cars sold and revenues in hopes of developing a predictive model in the near
future. Below is the number of cars sold and revenue generated for 6 automotive
dealerships. You're expected to create a SCATTERPLOT diagram, then insert a line of
best fit and the regression equation.
Company Cars (in ten thousands) Revenue (in billions)
A 63 7
B 29 3.9
C 20.8 2.1
D 19.1 2.8
E 13.4 1.4
F 8.5 1.5
Please provide your interpretation of results. For example, you might want to describe the direction of
the relationship between the X and Y variables. You may also want to share your thoughts regarding
the strength of the relationship. This will be reflected in how closely the data points cluster around the
line of best fit. Finally, you would probably want to make reference to the r2, and narratively interpret
this rate. You may also want to share some relevant descritpive statistics on the cars and revenues.

Solutions

Expert Solution

yes car(in ten thousand) and revenue are possitively correlated

Correlations          
       cars(in ten thousand) and  Revenue(in billion) Pearson Correlation is 0 .982

The most of the point are near to straight line so model is normally disrtibuted

the R sqaure value is  0.9643 means the model is good fit

descriptive statistics

Call:
lm(formula = y ~ x)

Residuals:
1 2 3 4 5 6
-0.08222 0.42604 -0.50373 0.37669 -0.41840 0.20161

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.39632 0.31913 1.242 0.282117
x 0.10613 0.01021 10.392 0.000484 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.4471 on 4 degrees of freedom
Multiple R-squared: 0.9643, Adjusted R-squared: 0.9554
F-statistic: 108 on 1 and 4 DF, p-value: 0.0004842


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