TSmith_Deliverable 6 - Analysis with Correlation and Regressionfinal

Magnitude Depth 2.74 7.5 0.74 2.5 0.64 14.0 Calculations 3.20 15.5 r 0.29966 0.70 3.0 slope 2.025822 2.20 2.4 y-intercept 5.990001 1.98 14.4 0.64 5.7 2.04 6.1 0.50 7.1 2.40 17.2 1.32 8.7 3.17 9.3 0.90 12.3 1.76 9.8 0.98 7.4 1.24 17.1 0.01 10.3 0.65 5.0 1.46 19.1 1.62 12.7 1.83 4.7 0.99 6.8 1.56 6.0 0.40 14.6 1.28 4.9 3.00 19.1 1.00 9.9 0.54 16.1 1.25 4.6 0.92 5.1 1.11 16.3 0.79 14.0 0.79 4.2 1.56 5.4 1.01 5.9 3.01 15.6 2.50 7.9 1.79 16.4 1.25 15.4 1.49 4.9 0.84 8.1 1.42 7.5 1.00 14.1 1.25 11.1 1.42 14.8

1.27 4.9 1.45 7.1 0.40 3.1 1.39 5.3 2.40 6.9 0.98 10.1 0.34 3.2 1.44 4.8 1.20 3.6 0.55 1.6 0.60 1.8 1.82 4.4 0.31 1.0 1.16 3.5

n the ntal ar the essed exts hmic ents any esults.

r CV of r 2a. Calculate the value of the linear correlation coefficient r and the critical value of r using α = 0.05. Show your calculations for r below. Include an explanation on how you found the critical value. Using Excel's CORREL function, one may determine the correlation coefficient r between two variables, w out to be r=0.29966. A t-distribution based method was employed to determine the critical value (CV) of r. Considering a sign and a sample size of n. I used T.INV(1-α/2, n-2) to get the critical t-value. =(T.INV(C14,C13-2))/SQRT((C14,C13-2))^2+C13-2) The border of r for our significance level is determined by this formula; if our computed r is greater than statistically significant.R's CV produced 0.214383. 2b. Determine whether there is sufficient evidence to support the claim of a linear correlation betwee magnitudes and the depths from the earthquakes. Explain your answer. The critical value (CV) is r=0.214383, while the correlation coefficient is r=0.29966. As 0.29966 > 0.214383 in this instance, there is enough data to substantiate the assertion of a linear rela between the earthquake depths and magnitudes at the α=0.05 level. This indicates that in the event that there is no real association, there is less than a 5% chance of seeing correlation by coincidence.

slope 2.025822 y-intercept 5.990001 R square 0.089796 3a. Find the regression equation. Let the predictor ( x ) variable be the magnitude. Identify the slope an Show your calculations below. Describe how you constructed the regression equation. =SLOPE(Depths ,Magnitude)=2.0258 =INTERCEPT (Depths ,Magnitude) =5.99 The regression equation represents the relationship between a predictor variable (x) and a response variable (y). The slope of the regression line is found using =SLOPE(y_range, x_range), which in this case is =SLOPE(Depths, Magnitude) an variable (y) is expected to increase when the predictor variable (x) increases by one unit. The y-intercept of the regression line is found using =INTERCEPT(y_range, x_range), which in this case is =INTERCEPT(Dept response variable (y) when the predictor variable (x) is zero. The regression equation that predicts the depth of an earthquake (y) based on its magnitude (x) would be: Depth = 2.0258 × Magnitude + 5.99 According to the slope, the depth should rise by about 2.0258 units for every unit increase in amplitude. The model appears to predict a positive depth when the magnitude is zero, based on the positive y-intercept. 3b. Is the equation a good model? Explain your answer. 0.089796 is the coefficient of determination. With an R2 value of 0.089796, the independent variable (the magnitude of the earthquakes) ca 8.98% of the variance in the dependent variable, which in your case is the depth of the earthqu regression model does not appear to fit the data very well, based on the comparatively low R2 v only a minor portion of the variation in the depth of the earthquakes can be explained by their 3c. What would be the best predicted depth of an earthquake with a magnitude of 1.26? Include the c Show your calculations below. Explain how you determined your answer. Using the regression equation: Depth = 2.0258 × Magnitude + 5.99 For an earthquake with a magnitude of 1.26, the best-predicted depth would be: Predicted Depth = (2.0258×1.26) + 5.99 =8.5425 Thus, the best predicted depth for an earthquake of magnitude 1.26 is approximately 8.5425 units.

nd the y-intercept within your regression equation. nd is equal to 2.0258. The slope indicates how much the response ths, Magnitude) and is equal to 5.99. The y-intercept is the value of the an account for around uakes. The linear value. Stated differently, magnitude. correct units.