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According to the U.S. Geological Survey (USGS), the probability of a magnitude 6.7 or greater earthquake in the Greater Bay Area is 63%, about 2 out of 3, in the next 30 years. In April 2008, scientists and engineers released a new earthquake forecast for the State of California called the Uniform California Earthquake Rupture Forecast (UCERF).
As a junior analyst at the USGS, you are tasked to determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and depths from the earthquakes. Your deliverables will be a PowerPoint presentation you will create summarizing your findings and an excel document to show your work.
Concept being Studied
- Correlation and regression
- Creating scatterplots
- Constructing and interpreting a Hypothesis Test for Correlation using r as the test statistic
You are given a spreadsheet that contains the following information:
- Magnitude measured on the Richter scale
- Depth in km
Using the spreadsheet, you will answer the problems below in a PowerPoint presentation.
What to Submit
The PowerPoint presentation should answer and explain the following questions based on the spreadsheet provided above.
- Slide 1: Title slide
- Slide 2: Introduce your scenario and data set including the variables provided.
- Slide 3: Construct a scatterplot of the two variables provided in the spreadsheet. Include a description of what you see in the scatterplot.
- Slide 4: Find the value of the linear correlation coefficient r and the critical value of r using Î± = 0.05. Include an explanation on how you found those values.
- Slide 5: Determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and the depths from the earthquakes. Explain.
- Slide 6: Find the regression equation. Let the predictor (x) variable be the magnitude. Identify the slope and the y-intercept within your regression equation.
- Slide 7: Is the equation a good model? Explain. What would be the best predicted depth of an earthquake with a magnitude of 2.0? Include the correct units.
- Slide 8: Conclude by recapping your ideas by summarizing the information presented in context of the scenario.
Along with your PowerPoint presentation, you should include your Excel document which shows all calculations.
Which of the following is not a correct value for a linear correlation coefficient for sample data r?
c. – 0.95
A correlation coefficient of -0.95 indicates what kind of relations between the two variables?
a. Strong positive correlation
b. Weak negative correlation
c. Strong negative correlation
d. No correlation
The relationship between coefficient of correlation and coefficient of determination is that:
a. They are unrelated
b. The coefficient of determination is the coefficient of correlation squared
c. The coefficient of correlation is the coefficient of determination squared
d. They are equal
When determining whether a correlation exists, it is a good idea to first explore the data by plotting a scatter plot.
a. The strength of correlation between the dependent and independent variables
b. The difference between two variables
c. Standard error of estimate
d. The percent of variations in the dependent variable explained by the independent variables
Regression equations are often useful for predicting the value of one variable, given a value of the other variable.
Which one of the following values is not required to calculate the correlation coefficient r?
a. The number of pairs of sample data n
b. The sum of all values of x Î£x
c. The sum of all values of x2y2 Î£x2y2
d. The sum of x multiplied by y Î£xy
The most commonly used formula to describe the linear regression is:
Which of the following is not a name for the straight line that best fits the scatter plot of paired sample data?
a. Regression line
b. Line of best fit
c. Scatter line
d. Least-squares line
A correlation exists between two variables only when the values of one variable are very strongly associated with the values of the other variable.
Which of the following is not a property of the linear correlation coefficient r?
a. – 1 â‰¤ r â‰¤ 1
b. x and y are interchangeable
c. r is a measurement of the strength of a linear relationship
d. r is not sensitive to outliers
If we determine that there is a correlation between poverty rate and crime rate in a city, then we can conclude that the increase in poverty causes people to commit more crime.
If the regression equation is not a good model, means there is no linear correlation, how can we use a sample to find the predicted value of y?
a. Use the mean of the actual y values
b. Use the mode of the actual y values
c. Use the median of the actual y values
d. We cannot use sample data to make any predictions
If the absolute value of correlation coefficient |r| is bigger than the critical value, which of the following conclusions is correct?
a. There is no sufficient evidence to support the claim of a linear correlation.
b. There is sufficient evidence to support the claim of a linear correlation.
c. There may or may not be a linear correlation between the two variables.
d. There is sufficient evidence to support the claim of a non-linear correlation.
When we interpret the determination coefficient r2, we are saying that
a. For each unit increase in x, we will see an increase or decrease in the predicted variable y
b. The sample is significantly different from the population
c. There is a strong positive or negative relationship between the variables
d. Some portion of the dependent variable co-varies with some portion of the independent variable
Predicted y = 20000 + 650x, where x = years of post-secondary educations and y = starting annual income. How is this regression equation interpreted?
a. For every year increase in income, education increases by $650.
b. For every year increase in education, expected starting income increases by $650.
c. For every year increase in education, expected starting income decreases by $650.
d. If x were equal to zero, income would be predicted to be $650.
When two variables are not related at all, how would you attach a quantitative measure to that situation?
a. Correlation coefficient r<0
b. Correlation coefficient râ‰¤0
c. Correlation coefficient r=0
d. No quantitative measure exists
How will you construct a hypothesis test for correlation using r as the test statistic?
a. H0: Ï = 0 (no correlation); Ha: Ï â‰ 0 (there is a correlation)
b. H0: r = 0 (no correlation); Ha: r â‰ 0 (there is a correlation)
c. H0: Ïâ‰ 0 (no correlation); Ha: Ï = 0 (there is a correlation)
d. H0: Ïâ‰ 0 (there is a correlation); Ha: Ï = 0 (no correlation)
The value of determination coefficient r2 indicates the proportion of the variation in y that is explained by the linear relationship between x and y.
What is a correct conclusion when | r | â‰¤ critical value?
a. Reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation.
b. Fail to reject the null hypothesis and conclude that there is no sufficient evidence to support the claim of a linear correlation.
c. Fail to reject the null hypothesis and conclude there is sufficient evidence to support the claim of a linear correlation.
d. Reject the null hypothesis and conclude that there is no sufficient evidence to support the claim of a linear correlation.