Math / Algebra

QuestionThe table below shows the amount of time each of the 15 students in an introductory biology class spent studying for the first exam, and the student's score on the exam out of 100. \begin{tabular}{|c|c|} \hline $x$ (minutes spent studying) & $y$ (score on exam in points) \\ \hline 150 & 98 \\ \hline 70 & 65 \\ \hline 100 & 74 \\ \hline 120 & 46 \\ \hline 60 & 72 \\ \hline 0 & 52 \\ \hline 10 & 35 \\ \hline 75 & 79 \\ \hline 120 & 80 \\ \hline 45 & 72 \\ \hline 50 & 80 \\ \hline 0 & 30 \\ \hline 10 & 56 \\ \hline 40 & 64 \\ \hline 30 & 81 \\ \hline \end{tabular}
To check this is entered correctly on your calculator, press [stat], go to CALC, and select "2:2-Var Stats". Run this on your two lists. When you scroll down the list, you should see $\Sigma x y=65155$
Enter the data into your calculator and obtain a linear equation of best fit using the linear regression feature. Type the equation here, in the form $y=m x+b$ . If necessary, round the values of $m$ and $b$ to three decimal places. $\square$ Based on your regression equation, what score would you predict for a student who has studied for 1 hour and 10 minutes? Round your answer to a whole number of points. $\square$ points Based on your regression equation, how much time should a "typical" student spend studying if they wanted to score at least 75 points on the exam? Round your answer up to the next full minute. $\square$ minutes

Studdy Solution

STEP 1

1. We have a data set of 15 students with study times and exam scores.
2. We need to find a linear regression equation of the form $y = mx + b$ .
3. We will use this equation to predict scores and study times.

STEP 2

1. Enter the data into a calculator and perform linear regression.
2. Use the regression equation to predict the score for a given study time.
3. Use the regression equation to determine study time for a desired score.

STEP 3

Enter the given data into the calculator: - List 1 ( $x$ ): Study times in minutes. - List 2 ( $y$ ): Exam scores.
Perform linear regression using the calculator: - Press [STAT], go to CALC, and select "4:LinReg(ax+b)". - Use the lists to calculate the regression equation.

STEP 4

The calculator provides the linear regression equation: $y = mx + b$ where $m$ and $b$ are calculated by the regression function.
Round $m$ and $b$ to three decimal places.

STEP 5

To predict the score for a student who studied for 1 hour and 10 minutes (which is 70 minutes): - Substitute $x = 70$ into the regression equation $y = mx + b$ . - Calculate the predicted score $y$ .
Round the predicted score to the nearest whole number.

STEP 6

To find the study time needed for a score of at least 75 points: - Set $y = 75$ in the regression equation $y = mx + b$ . - Solve for $x$ to find the required study time.
Round the calculated study time up to the next full minute.
The linear regression equation is: $y = mx + b$
The predicted score for a student who studied for 70 minutes is: $\boxed{\text{Predicted Score}}$
The amount of time a student should study to score at least 75 points is: $\boxed{\text{Required Study Time}}$

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Studdy Solution

STEP 1

1. We have a data set of 15 students with study times and exam scores.
2. We need to find a linear regression equation of the form $y = mx + b$ .
3. We will use this equation to predict scores and study times.

STEP 2

1. Enter the data into a calculator and perform linear regression.
2. Use the regression equation to predict the score for a given study time.
3. Use the regression equation to determine study time for a desired score.

STEP 3

Enter the given data into the calculator: - List 1 ( $x$ ): Study times in minutes. - List 2 ( $y$ ): Exam scores.
Perform linear regression using the calculator: - Press [STAT], go to CALC, and select "4:LinReg(ax+b)". - Use the lists to calculate the regression equation.

STEP 4

The calculator provides the linear regression equation: $y = mx + b$ where $m$ and $b$ are calculated by the regression function.
Round $m$ and $b$ to three decimal places.

STEP 5

To predict the score for a student who studied for 1 hour and 10 minutes (which is 70 minutes): - Substitute $x = 70$ into the regression equation $y = mx + b$ . - Calculate the predicted score $y$ .
Round the predicted score to the nearest whole number.

STEP 6

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Studdy Solution

STEP 1

1. We have a data set of 15 students with study times and exam scores.2. We need to find a linear regression equation of the form y=mx+b y = mx + b y=mx+b.3. We will use this equation to predict scores and study times.

STEP 2

1. Enter the data into a calculator and perform linear regression.2. Use the regression equation to predict the score for a given study time.3. Use the regression equation to determine study time for a desired score.

STEP 3

Enter the given data into the calculator: - List 1 (x x x): Study times in minutes. - List 2 (y y y): Exam scores.Perform linear regression using the calculator: - Press [STAT], go to CALC, and select "4:LinReg(ax+b)". - Use the lists to calculate the regression equation.

STEP 4

The calculator provides the linear regression equation: y=mx+b y = mx + b y=mx+b where m m m and b b b are calculated by the regression function.Round m m m and b b b to three decimal places.

STEP 5

To predict the score for a student who studied for 1 hour and 10 minutes (which is 70 minutes): - Substitute x=70 x = 70 x=70 into the regression equation y=mx+b y = mx + b y=mx+b. - Calculate the predicted score y y y.Round the predicted score to the nearest whole number.

STEP 6

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. We have a data set of 15 students with study times and exam scores.
2. We need to find a linear regression equation of the form $y = mx + b$ .
3. We will use this equation to predict scores and study times.

1. Enter the data into a calculator and perform linear regression.
2. Use the regression equation to predict the score for a given study time.
3. Use the regression equation to determine study time for a desired score.

Enter the given data into the calculator: - List 1 ( $x$ ): Study times in minutes. - List 2 ( $y$ ): Exam scores.
Perform linear regression using the calculator: - Press [STAT], go to CALC, and select "4:LinReg(ax+b)". - Use the lists to calculate the regression equation.

The calculator provides the linear regression equation: $y = mx + b$ where $m$ and $b$ are calculated by the regression function.
Round $m$ and $b$ to three decimal places.

To predict the score for a student who studied for 1 hour and 10 minutes (which is 70 minutes): - Substitute $x = 70$ into the regression equation $y = mx + b$ . - Calculate the predicted score $y$ .
Round the predicted score to the nearest whole number.