# T-tests and Regressions

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1) You are estimating the cost of optical sensors based on the POWER OUTPUT of the sensor. You

decide to calculate the coefficient of determination (R2) as part of determining the goodness of fit of

an equation. Using the preliminary calculations below, calculate the R2 and determine its meaning.

a. 4.67% of the variation in the cost is being explained by the power.

b. 95.33% of the variation in the power is being explained by the cost.

c. 95.33% of the variation in the cost is being explained by the power.

d. 4.67% of the variation in the power is being explained by the cost.

2) You are estimating the cost ($K) of optical sensors based on the radius of the sensors. Using the

preliminary calculations from a data set of 8 sensors, determine the equation of the line. (Round your

intermediate calculations to 3 decimal places) SY = 2575 SX=21 SXY=9105 SX2=102

a. Cost = - 63.277 + 111.897 (Radius)

b. Cost = 50.040 + 190.520 (Radius)

c. Cost = 1.908 + 307.936 (Radius)

d. Cost = 190.520 + 50.040 (Radius)

3) A coworker is considering the use of a log linear (power) model using weight to estimate the cost

of a manufacturing effort. They have performed the following calculations in LOG SPACE using

natural logarithms. Select the corresponding UNIT SPACE form of this power model equation.

Log Space b1 = 1.455294 b0 = 3.673610

a. Cost = 39.393861 (Weight)1.455294

b. Cost = 1.455294 + 3.939388 (Weight)

c. Cost = 3.939388 + 1.455294 (Weight)

d. Cost = 51.387143 (Weight)1.455294

4) You are estimating the manufacturing hours for an airframe based on the airframe weight. The

airframe you are estimating weighs 141784 pounds. Given the following equation, select the correct

response from each pair. Hours = 124.50 + 0.75 (Weight in pounds)

- The independent variable is Hours

- The independent variable is Weight

- The slope is 124.50

- The slope is 0.75DAU

- The estimated manufacturing hours for your airframe are 762 hours

- The estimated manufacturing hours for your airframe are 106462.5 hours

5) You have calculated the following POWER model and associated UNIT SPACE values:

a. Power equation because it has a lower standard error than the linear model.

b. Linear equation because it has a higher standard error than the power model.

c. Linear equation because it has a lower standard error than the power model.

d. Power equation because it has a higher standard error than the linear model.

6) Given a one independent variable linear equation that states cost in $K, and given the following

information, calculate the STANDARD ERROR and determine its meaning.

a. If we used this equation, we could typically expect to be off by ± 42.83%.

b. If we used this equation, we could typically expect to be off by ± $42.83K.

c. If we used this equation, we could typically expect to be off by ± 37.09%.

d. If we used this equation, we could typically expect to be off by ± $37.09K.

7) You are trying to determine the statistical significance of an equation. Given the following

information, test the slope of the equation at the 90% level of confidence. Select the correct answer

out of each pair of choices. Cost = - 76.25 + 114.82 (Range) n=9 Sb1=17.669

- The tp is 1.895

- The tp is 2.365

- The tc is 4.315

- The tc is 6.498

We would REJECT the null hypothesis

We would FAIL TO REJECT the null hypothesis

We would consider using the equation

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Solutions:

1. R^2 is calculated as regression sums of squares / total sums of squares. Thus,

R^2 = 6874/147172 = 4.67%

Our model is trying to explain the cost of optical sensors, so the answer is:

(A) 4.67% of the variation in the cost is being explained by the power.

2. The slope b can be calculated by

b = (Sxy - 1/8*Sx*Sy)/(Sx^2-1/8*(Sx)^2) = 50.04

The intercept a is given by:

a = 1/8(Sy-b*Sx) = 190.52

(D) Cost = 190.520 + ...

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