Question

An insurance firms wants to examine the relationship between text messages per day and insurance claims. The following data is a sample of 5 participants:

Cellphone Texts per day (X) Insuance Claims ($$) (Y)
4 800
18 2600
12 2800
26 0
20 6000

Choose the correct Estimated Regression Equation.

Answer 1

If you need to show the work by hand, you can develop the regression equation in the following format:

predicted y = a + bx
...where a represents the y-intercept and b the slope.

To get to that point, here are some formulas to calculate along the way.

To find a:
a = (Ey/n) - b(Ex/n)

Note: E here means to add up or to find the total.

To find b:
b = SSxy/SSxx

To find SSxy:
SSxy = Exy - [(Ex)(Ey)]/n

To find SSxx:
SSxx = Ex^2 - [(Ex)(Ex)]/n

I hope this will help get you started.

Answer 2

37

Answer 3

80%

Answer 4

[AI-generated answer — Explain Bot]

To determine the estimated regression equation, we need to find the line that best fits the given data points. This can be done using linear regression analysis.

Step 1: Calculate the means of X and Y:
The mean of X = (4 + 18 + 12 + 26 + 20) / 5 = 16
The mean of Y = (800 + 2600 + 2800 + 0 + 6000) / 5 = 2440

Step 2: Calculate the deviations from the mean for X and Y:
Deviation of X = (X - X_mean) = (4 - 16), (18 - 16), (12 - 16), (26 - 16), (20 - 16) = -12, 2, -4, 10, 4
Deviation of Y = (Y - Y_mean) = (800 - 2440), (2600 - 2440), (2800 - 2440), (0 - 2440), (6000 - 2440) = -1640, 160, 360, -2440, 3560

Step 3: Calculate the product of deviations for X and Y:
Product of deviations = (Deviation of X) * (Deviation of Y) = (-12) * (-1640), (2) * (160), (-4) * (360), (10) * (-2440), (4) * (3560) = 19680, 320, -1440, -24400, 14240

Step 4: Calculate the squared deviations for X:
Squared deviation of X = (Deviation of X)^2 = (-12)^2, (2)^2, (-4)^2, (10)^2, (4)^2 = 144, 4, 16, 100, 16

Step 5: Calculate the sum of squared deviations for X and Y:
Sum of squared deviations of X = sum(Squared deviation of X) = 144 + 4 + 16 + 100 + 16 = 280
Sum of squared deviations of Y = sum((Deviation of Y)^2) = 1640^2 + 160^2 + 360^2 + 2440^2 + 3560^2 = 11296000

Step 6: Calculate the slope of the regression line:
Slope (b) = (sum(Product of deviations)) / (sum(Squared deviation of X)) = 19680 / 280 = 70.2857

Step 7: Calculate the intercept of the regression line:
Intercept (a) = Y_mean - (b * X_mean) = 2440 - (70.2857 * 16) = 1362.857

Step 8: Write the estimated regression equation:
Estimated Regression Equation: Y = a + bX
Y = 1362.857 + 70.2857X

Therefore, the correct estimated regression equation for this data is Y = 1362.857 + 70.2857X.