a)
Independent variable (X) = Magnitude of earth quake
Dependent variable (Y) = Depth of quake
b)
Regression line:
Y^ = b+m*X (Single independent variable)
c)
Excel > Data > Data Analysis > Regression
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.026974584 | |||||||
R Square | 0.000727628 | |||||||
Adjusted R Square | -0.054787504 | |||||||
Standard Error | 2.986219457 | |||||||
Observations | 20 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1 | 0.116880366 | 0.116880366 | 0.013106844 | 0.910120618 | |||
Residual | 18 | 160.5151196 | 8.917506646 | |||||
Total | 19 | 160.632 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 7.622721633 | 3.067158648 | 2.485271389 | 0.023000926 | 1.178860429 | 14.06658284 | 1.178860429 | 14.06658284 |
Magnitude (X) | -0.091028322 | 0.795110481 | -0.114485124 | 0.910120618 | -1.761493456 | 1.579436811 | -1.761493456 | 1.579436811 |
Intercept (b) = 7.6227
Slope (m) = -0.0910
Regression equation:
Y^ = 7.6227-0.0910*X
d)
If X = 3.3
Y^ = 7.6227-0.0910*X
Y^ = 7.6227-0.0910*3.3 = 7.3224
e)
Y = 5.3 when X = 3.3
Y^ = 7.3224
Residual = Y-Y^ = 5.3-7.3224 = -2.0224
f)
i)
Hypothesis:
H0: β1 = 0
Ha: β1 not = 0
ii)
ANOVA | |||||
df | SS | MS | F | Significance F | |
Regression | 1 | 0.116880366 | 0.116880366 | 0.013106844 | 0.910120618 |
Residual | 18 | 160.5151196 | 8.917506646 | ||
Total | 19 | 160.632 |
iii)
Fcritical = 4.4139
Rejection region:
If Fstat > Fcritical, reject H0
iv)
Fstat < Fcritical, Do not reject H0
P value = 0.9101 > 0.05, Do not reject H0
There is not enough evidence to conclude that regression model is statistically significant at 5% significance level
Note:
Calculations:
X | Y | X^2 | Y^2 | XY | ||||
3.9 | 8.8 | 15.21 | 77.44 | 34.32 | ||||
4.3 | 10 | 18.49 | 100 | 43 | ||||
3.3 | 11.2 | 10.89 | 125.44 | 36.96 | ||||
4.6 | 9.5 | 21.16 | 90.25 | 43.7 | ||||
3.9 | 12.8 | 15.21 | 163.84 | 49.92 | ||||
3.2 | 3.9 | 10.24 | 15.21 | 12.48 | ||||
3.4 | 5.5 | 11.56 | 30.25 | 18.7 | ||||
4.5 | 7.1 | 20.25 | 50.41 | 31.95 | ||||
5.1 | 8.5 | 26.01 | 72.25 | 43.35 | ||||
2.6 | 7.9 | 6.76 | 62.41 | 20.54 | ||||
3.3 | 5.3 | 10.89 | 28.09 | 17.49 | ||||
3 | 5 | 9 | 25 | 15 | ||||
4.5 | 6.5 | 20.25 | 42.25 | 29.25 | ||||
2.9 | 7.6 | 8.41 | 57.76 | 22.04 | ||||
4.5 | 10 | 20.25 | 100 | 45 | ||||
2.8 | 5 | 7.84 | 25 | 14 | ||||
5.1 | 4 | 26.01 | 16 | 20.4 | ||||
4.7 | 3 | 22.09 | 9 | 14.1 | ||||
3.5 | 3 | 12.25 | 9 | 10.5 | ||||
2.2 | 11 | 4.84 | 121 | 24.2 | ||||
SUM | 75.3 | 145.6 | 297.61 | 1220.6 | 546.9 | |||
n | 20 | |||||||
Mean | 3.765 | 7.28 | ||||||
k | 2 | |||||||
SSxx | 14.1055 | Sum(x^2) - ((Sum(x))^2 /n) | SSR | 0.11688 | slope * Ssxy | MSR | 0.11688 | SSR/k-1 |
Ssyy | 160.632 | Sum(y^2) - ((Sum(y))^2 /n) | SSE | 160.5151 | SST-SSR | MSE | 8.917507 | SSE/n-k |
Ssxy | -1.284 | Sum(xy) - (Sum(x)*Sum(y)/n) | SST | 160.632 | Ssyy | F | 0.013107 | MSR/MSE |
slope | -0.09103 | Ssxy/SSxx | ||||||
intercept | 7.622722 | Mean Y - Mean X * Slope | ||||||
Se | 2.986219 | SQRT(SSE/(n-2)) | ||||||
Sb1 | 0.79511 | Se/SQRT(SSxx) | ||||||
r | -0.02697 | Ssxy/SQRT(SSxx*Ssyy) | ||||||
r^2 | 0.000728 |
Question 164 points): Is the magnitude of an earthquake related to the depth below the surface...
Question 1: Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? In order to answer this question an analysis is conducted. Let we wish to explain depth (in kilometers) of the quake below the surface at the epicenterx by magnitude of an earthquake (on the Richter scale). Data are as follows: 1 2 3 4 5 6 7 8 9 10 3.9 4.3 3.3 4.6 3.9 3.2 3.4 4.5 5.1 2.6...
Question 1 : Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? In order to answer this question an analysis is conducted. Let we wish to explain depth (in kilometers) of the quake below the surface at the epicenterx by magnitude of an earthquake (on the Richter scale). Data are as follows: 1 2 3 4 5 6 7 8 9 10 3.9 4.3 3.3 4.6 3.9 3.2 3.4 4.5 5.1...
Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter. x 3.4 4.6 3.3 4.5 2.6 3.2 3.4 y 5.3 10.3 11.2 10.0 7.9 3.9 5.5 (a) Make a scatter diagram of the data. (b) Use a calculator to verify that Σx =...
Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter. x 3.1 4.6 3.3 4.5 2.6 3.2 3.4 y 4.8 9.8 11.2 10.0 7.9 3.9 5.5 (a) Make a scatter diagram of the data. Then visualize the line you think best fits the...
Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter. x 3.5 4.4 3.3 4.5 2.6 3.2 3.4 y 4.5 10.4 11.2 10.0 7.9 3.9 5.5 (a) Make a scatter diagram of the data. Get Flash Player Flash Player version 10 or higher...
35 6. (15 points) Data from the United States Geological Survey can be used to predict the magnitude of earthquakes based on the depth of the fault below the surface. The magnitude is given according to the Richter scale and the depth is in kilometers. magnitude 7.7 6.7 6.9 6.8 4.0 3.8 7.1 5.9 depth 18 17 26 5 10 23 10 The standard deviation for the magnitude is 1.45, and the standard deviation for the depth is 9.83. The...
(b) Construct a frequency distribution showing the class limits for the four classes (c) Construct a bar-chart. 13/ The following gave the sample data on caffeine per ounce for 6 top-energy drinks 10, 10, 9, 11, 15, 8 a/Compute the mean b/Compute sample standard deviation. c/Find 5 number summary 14/Calculate the range, mean, median, first and third quartiles, mode for the following datasets: 47, 59, 50, 56, 56, 51, 52, 53 15/Find the mean, the range, 5 number summary and...
Please help with these questions. 5. (12 points) The United States Geological Survey is conducting a study to predict the magnitude of earthquakes based on the depth of the fault below the surface. The magnitudes of several earthquakes (as measured on the Richter scale) were recorded as part of this analysis, and the data is listed below. 7.1 7.7 5.9 6.7 6.9 8.2 2.1 6.8 4.0 6.5 6.7 3.8 5.6 (a) Find the median and quartiles of the data set....
It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. х 33 26 y48 44 14, Ey 151, x2 = 66, Ey2 = 6005, Exy Complete parts (a) through (e), given...
Question 3 (3 points) The table below shows the regression results when calculating the least squares line of regression relating variable x (predictor) to variable y (response): Intercept Coefficients 0.083 1.417 Standard Error 3.56 0.63 t Star 0.02 2.25 P-value 0.9822 0.0745 Does variable x share a statistically significant linear relationship with variable y at the 5% significance level? Yes, since the p-value of 0.0745 is greater than 0.05. Yes, since the slope coefficient of 1.417 is less than the...