# A multiple regression equation to predict a student's score in College Algebra (\hat{y}) based on their high school GPA (x_{1}), their high school Algebra II grade (x_{2}), and their placement test score (x_{3}) is given by the equation below. \hat{y}=-9+5x_{1}+6x_{2}+0.3x_{3} According to this equation, what does the student's placement test score need to be if their high school GPA was a 3.9, their high school Algebra II grade was a 2, and their predicted College Algebra score was a 67? Round to 1 decimal place.

Question
Upper level algebra
A multiple regression equation to predict a student's score in College Algebra $$\displaystyle{\left(\hat{{{y}}}\right)}$$ based on their high school GPA $$\displaystyle{\left({x}_{{{1}}}\right)}$$, their high school Algebra II grade $$\displaystyle{\left({x}_{{{2}}}\right)}$$, and their placement test score $$\displaystyle{\left({x}_{{{3}}}\right)}$$ is given by the equation below.
$$\displaystyle\hat{{{y}}}=-{9}+{5}{x}_{{{1}}}+{6}{x}_{{{2}}}+{0.3}{x}_{{{3}}}$$
According to this equation, what does the student's placement test score need to be if their high school GPA was a 3.9, their high school Algebra II grade was a 2, and their predicted College Algebra score was a 67? Round to 1 decimal place.

2021-01-28
Step 1
Given,
A multiple regression equation to predict a student's score in College Algebra $$\displaystyle{\left(\hat{{{y}}}\right)}$$ based on their high school GPA $$\displaystyle{\left({x}_{{{1}}}\right)}$$, their high school Algebra II grade $$\displaystyle{\left({x}_{{{2}}}\right)}$$, and their placement test score $$\displaystyle{\left({x}_{{{3}}}\right)}$$ is given by the equation below.
$$\displaystyle\hat{{{y}}}=-{9}+{5}{x}_{{{1}}}+{6}{x}_{{{2}}}+{0.3}{x}_{{{3}}}$$
Step 2
The student's placement test score need to be if their high school GPA was a 3.9, their high school Algebra II grade was a 2, and their predicted College Algebra score was a 67 is calculated as follows:
$$\displaystyle\hat{{{y}}}=-{9}+{5}{x}_{{{1}}}+{6}{x}_{{{2}}}+{0.3}{x}_{{{3}}}$$
$$\displaystyle{67}=-{9}+{5}{\left({3.9}\right)}+{6}{\left({2}\right)}+{0.3}{x}_{{{3}}}$$
$$\displaystyle{67}={22.5}+{0.3}{x}_{{{3}}}$$
$$\displaystyle{44.5}={0.3}{x}_{{{3}}}$$
$$\displaystyle{x}_{{{3}}}={\frac{{{44.5}}}{{{0.3}}}}={148.3}$$
The student's placement test score need to be 148.3.

### Relevant Questions

A multiple regression equation to predict a student's score in College Algebra $$\displaystyle{\left(\hat{{{y}}}\right)}$$ based on their high school GPA $$\displaystyle{\left({x}_{{{1}}}\right)}$$, their high school Algebra II grade $$\displaystyle{\left({x}_{{{2}}}\right)}$$, and their placement test score $$\displaystyle{\left({x}_{{{3}}}\right)}$$ is given by the equation below.
$$\displaystyle\hat{{{y}}}=-{9}+{5}{x}_{{{1}}}+{6}{x}_{{{2}}}+{0.3}{x}_{{{3}}}$$
According to this equation, what is the predicted value of the student's College Algebra score if their high school GPA was a 3.9, their high school Algebra II grade was a 2 and their placement test score was a 40? Round to 1 decimal place.
A multiple regression equation to predict a student's score in College Algebra $$(\hat{y})$$ based on their high school GPA (x1x1), their high school Algebra II grade (x2x2), and their placement test score (x3x3) is given by the equation below.
$$\hat{y}=-9+5x1x1+6x2x2+0.3x3x3$$
a) According to this equation, what is the predicted value of the student's College Algebra score if their high school GPA was a 3.9, their high school Algebra II grade was a 2 and their placement test score was a 40? Round to 1 decimal place.
b) According to this equation, what does the student's placement test score need to be if their high school GPA was a 3.9, their high school Algebra II grade was a 2, and their predicted College Algebra score was a 67? Round to 1 decimal place.
Case: Dr. Jung’s Diamonds Selection
With Christmas coming, Dr. Jung became interested in buying diamonds for his wife. After perusing the Web, he learned about the “4Cs” of diamonds: cut, color, clarity, and carat. He knew his wife wanted round-cut earrings mounted in white gold settings, so he immediately narrowed his focus to evaluating color, clarity, and carat for that style earring.
After a bit of searching, Dr. Jung located a number of earring sets that he would consider purchasing. But he knew the pricing of diamonds varied considerably. To assist in his decision making, Dr. Jung decided to use regression analysis to develop a model to predict the retail price of different sets of round-cut earrings based on their color, clarity, and carat scores. He assembled the data in the file Diamonds.xls for this purpose. Use this data to answer the following questions for Dr. Jung.
1) Prepare scatter plots showing the relationship between the earring prices (Y) and each of the potential independent variables. What sort of relationship does each plot suggest?
2) Let X1, X2, and X3 represent diamond color, clarity, and carats, respectively. If Dr. Jung wanted to build a linear regression model to estimate earring prices using these variables, which variables would you recommend that he use? Why?
3) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
4) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
5) Dr. Jung now remembers that it sometimes helps to perform a square root transformation on the dependent variable in a regression problem. Modify your spreadsheet to include a new dependent variable that is the square root on the earring prices (use Excel’s SQRT( ) function). If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?
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6) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
7) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must actually square the model’s estimates to convert them to price estimates.) Which sets of earring appears to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
8) Dr. Jung now also remembers that it sometimes helps to include interaction terms in a regression model—where you create a new independent variable as the product of two of the original variables. Modify your spreadsheet to include three new independent variables, X4, X5, and X6, representing interaction terms where: X4 = X1 × X2, X5 = X1 × X3, and X6 = X2 × X3. There are now six potential independent variables. If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?
9) Suppose Dr. Jung decides to use color (X1), carats (X3) and the interaction terms X4 (color * clarity) and X5 (color * carats) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
10) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must square the model’s estimates to convert them to actual price estimates.) Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Total:
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
a) What percent are Black?
b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P $$(A and B) = P(A) \cdot P(B) P(A and B) = P(A) \cdot P(B).$$
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
g) What percent of blacks shot and killed by police were unarmed?
h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
Do a search on the internet for reasons why blacks are more likely to be killed by police. Read a few articles on the topic. Write your response using the articles as references. Give the websites used in your response. Your answer should be several sentences long with at least one website listed. This part of this problem will be graded after the due date.
To find the lowest original score that will result in an A if the professor uses
$$(i)(f*g)(x)\ and\ (ii)(g*f)(x)$$.
Professor Harsh gave a test to his college algebra class and nobody got more than 80 points (out of 100) on the test.
One problem worth 8 points had insufficient data, so nobody could solve that problem.
a. Increasing everyone's score by 10% and
b. Giving everyone 8 bonus points
c. x represents the original score of a student
Students in a college algebra class were given a final exam in May and subsequently retested montly with an equivalant exam. The average score $$(\overline{x})$$ for the class is given by the human memory model $$\overline{x} = 86-15\log(t+1)$$
where t is the time in months after the final exam. What is the average score 5 months after the final exam? Give your answer correct to the nearest hundreth.
To calculate: The probability that the selected student was in the 37-46 are group or received a "B" in the course.
Given Information:
A table depicting the grade distribution for a college algebra class based on age and grade.
To calculate: The probability that the selected student was in the 27-36 are group.
Given Information:
A table depicting the grade distribution for a college algebra class based on age and grade.
$$H_{0}:\sigma=60,\ H_{1}:\sigma\ <\ 60H_{0}:\sigma\ >\ 60,\ H_{1}:\sigma=60H_{0}:\sigma=60,\ H_{1}:\sigma\ >\ 60H_{0}:\sigma=60,\ H_{1}:\sigma\ \neq\ 60$$