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# simplifying the square and finding values

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2. simplify the square of 96b(cubed)/144a(4th power)

3. Find the value(s) of b that would make the following true: 5b(squared)-125=0.

4. Solve using the quadratic formula: 2x(squared)+2x=3.

5. State the number of zeroes for each equation:
x(squared)=4x x(squared)+9=6x x(squared)+25=0

6. a model rocket is fired upward with an initial velocity of 36 ft/s from a height of 10 feet. Use the formula: h=16t(squared)+vt+s to determine when the ball will hit the ground(h is the height, v is the initial velocity, and s is the starting height)

7. Determine the x-intercepts using the quadratic formula: f(x)=6x(squared)-13x-5

8. The product of two consecutive, positive, ODD integers is 1295. Write an equation to describe this scenario and solve it.

9. The width of a rectangle is 3 times the length. The area is 12 square units. Write an equation to describe the scenario and solve it.

10. The population of a bee hive can be modeled by the function
P(x)=2x(squared) +11x+8. The graph of this function has 1 x-intercept. Is there any value of x that can make the hive have a population of 0 bees? Explain.

11. The area of a the triangle is 16 units(squared). Write an equation and find the value of x.

12. solve 4/8x-2=8/1-4x

13. solve for d : a/b=c/d

14. What is the common factor in the numerator and denominator?
64-x(squared)/x(squared)-x-56

15. Carol and Mike take their six children to the museum. The cost of admission for 2 adults and 6 kids is \$156. The next week, their maid Alice goes with them, but this time only 4 kids go along. The cost for 3 adults and 4 kids is \$144. Write a system of equations to describe this and determine the cost of one adult ticket.

16. Which point is a solution to the system of inequalities?
y>2x-3
2x+3y<(equal to)12

17. Simplify: 24p(to negative 4th power)q(to 0 power)r(squared)/4p(to -6 power)q(to -2 power)r(to - 6 power)

18. You join a fitness club. The first club charges a startup fee of \$72 plus \$22 per month. The second club charges no startup fee but charges \$25 per month. After how many months wil the cost be the same?

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#### Solution Preview

2. simplify the square of 96b(cubed)/144a(4th power)

Solution:

3. Find the value(s) of b that would make the following true: 5b(squared)-125=0.

Solution:

4. Solve using the quadratic formula: 2x(squared)+2x=3.

Solution:

5. State the number of zeroes for each equation:
x(squared)=4x x(squared)+9=6x x(squared)+25=0

Solution:

6. a model rocket is fired upward with an initial velocity of 36 ft/s from a height of 10 feet. Use the formula: h=16t(squared)+vt+s to determine when the ball will hit the ground(h is the height, v is the initial velocity, and s is the starting height)

Solution:

7. Determine the ...

#### Solution Summary

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## Simple and Multiple Linear Regression Calculations

See the attached file.

1. Use the following results obtained from a simple linear regression analysis with 15 observations.
Y ̂ = 35.5- (1.75)X
R2= 0.9345 and sb1 = 0.60

Interpret regression results and the value of the coefficient of Determination. Predict the value of Y when X is equal to 10. Calculated the correlation coefficient between Y and X. Test to determine if there is a significant relationship between the independent and dependent variable at  = 0.05. Perform a two-tailed test.
2. A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects past months of data consisting of tire sales (in hundreds of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 20 observations, the simple linear regression model yielded the following results. (X is advertising expenditure in thousand dollars and Y is tires sold in hundreds): ∑X = 50; ∑Y = 100; ∑X2 = 225; ∑Y2 = 720; ∑XY = 390.
Find the Intercept and slope and Write the Regression Equation. Also predict the amount of tires sold when money invested in advertising is 5 thousand dollars. Calculate the correlation coefficient and coefficient of determination. Check whether there is a relation between correlation coefficient and coefficient of determination. Calculate SSE and MSE, and standard error and t-score of the slope coefficient.

3. A member of the state legislature has expressed concern about the differences in the mathematics test scores of high school freshmen across the state. She asks her research assistant to conduct a study to investigate what factors could account for the differences. The research assistant looked at a random sample of school districts across the state and used the factors of percentage of mathematics teachers in each district with a degree in mathematics, the average age of mathematics teachers and the average salary of mathematics teachers:

Regression Output
Predictor Coef. SE Coef.
Constant 35.17 7.850
Math Degree (%) 0.30 0.080
Age 0.45 0.188
Salary 0.15 0.075

Analysis of Variance
Source DF SS
Regression 3 1120.5
Residual Error 28 530.8

Write the least squares prediction equation. What is the number of observations in the sample? Based on the multiple regression model given above, estimate the mathematics test score and calculate the value of the residual, if the percentage of teachers with a mathematics degree is 50.0, the average age is 45 and the average salary is \$48,000. If the actual mathematics test score for these factors is 68.50, what is the error for this observation? What is the total sum of squares? What is the explained variation? What is the mean square error and the standard error of estimate?
4. For the results given in question # 3 above, calculate the Coefficient of Determination and the Adjusted coefficient of Determination and Test for the overall usefulness of the model using F-Statistic at 5% and 1% significance levels. Finally, test the usefulness (or significance of the three independent variables using t-test for 5% and 1% significance levels.
5. The following table gives the data for per capita income in thousands of US dollars with the percentage of the labor force in Agriculture and the average years of schooling of the population over 25 years of age for 15 developed countries in 2000 (data modified for educational purpose). Develop a multiple regression model for per capita income (dependent variable) using Excel or MegaStat and answer the questions below the table. You can use symbols Y, X1 and X2 for the variables in your calculation. Show your computer output.
Country number per capita % of labor in Agriculture Average years of schooling
1 20 9 7
2 26 10 12
3 24 8 11
4 21 7 11
5 22 10 12
5 42 4 16
7 27 5 11
8 24 5 9
9 28 6 12
10 32 8 14
11 30 7 12
12 40 4 16
13 34 9 14
14 30 5 10
15 35 8 13

Find the Y-intercept and slopes for the two independent variables and interpret them. Predict the per capita income when percentage of labor force in Agriculture is only 3 and average years of schooling is 15. Find the overall explanatory power (Coefficient of Determination) of the model and interpret it. Also find the adjusted coefficient of Determination and interpret it. Find the standard error of estimate. From the ANOVA table find SSR, SSE and SST and the F-value. Perform the F-test and comment on the overall usefulness of the model Perform t-test for the statistical significance of individual coefficients.

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