Question Predict homework time from TV time using the linear equation $y=-0.76x+26.04$ for 23 students. (a) Predicted homework time for 12 hours of TV: $-0.76(12)+26.04=10.92$ hours. (b) Predicted homework time for 0 hours of TV: $-0.76(0)+26.04=26.04$ hours. (c) Predicted decrease in homework time for 1 hour increase in TV time: $-0.76$ hours.

Studdy Solution

STEP 1

Assumptions
1. The line of best fit equation is given by $y = -0.76x + 26.04$ .
2. The variable $x$ represents the time spent watching TV in hours.
3. The variable $y$ represents the time spent doing homework in hours.
4. The equation can be used to predict the time spent doing homework based on the time spent watching TV.

STEP 2

To find the predicted time spent doing homework for a student who spends 12 hours watching TV, we substitute $x = 12$ into the line of best fit equation.
$y = -0.76x + 26.04$

STEP 3

Now, plug in $x = 12$ into the equation.
$y = -0.76(12) + 26.04$

STEP 4

Calculate the value of $y$ when $x = 12$ .
$y = -0.76 \times 12 + 26.04$

STEP 5

Perform the multiplication.
$y = -9.12 + 26.04$

STEP 6

Calculate the predicted time spent doing homework for a student who spends 12 hours watching TV.
$y = 26.04 - 9.12$

STEP 7

Complete the subtraction to find the predicted time.
$y = 16.92$
The predicted time spent doing homework for a student who spends 12 hours watching TV is 16.92 hours.

STEP 8

To find the predicted time spent doing homework for a student who doesn't spend any time watching TV, we substitute $x = 0$ into the line of best fit equation.
$y = -0.76x + 26.04$

STEP 9

Now, plug in $x = 0$ into the equation.
$y = -0.76(0) + 26.04$

STEP 10

Calculate the value of $y$ when $x = 0$ .
$y = 0 + 26.04$

STEP 11

Since multiplying by zero gives zero, the predicted time spent doing homework is simply the constant term of the equation.
$y = 26.04$
The predicted time spent doing homework for a student who doesn't spend any time watching TV is 26.04 hours.

STEP 12

To find the predicted decrease in the time spent doing homework for an increase of one hour in the time spent watching TV, we look at the coefficient of $x$ in the line of best fit equation.
$y = -0.76x + 26.04$

STEP 13

The coefficient of $x$ is $-0.76$ , which represents the change in $y$ (time spent doing homework) for each one-unit increase in $x$ (time spent watching TV).

STEP 14

Since the coefficient is negative, it indicates a decrease in the time spent doing homework.
The predicted decrease in the time spent doing homework for an increase of one hour in the time spent watching TV is 0.76 hours.

Was this helpful?

Studdy Solution

STEP 1

STEP 2

To find the predicted time spent doing homework for a student who spends 12 hours watching TV, we substitute $x = 12$ into the line of best fit equation.
$y = -0.76x + 26.04$

STEP 3

Now, plug in $x = 12$ into the equation.
$y = -0.76(12) + 26.04$

STEP 4

Calculate the value of $y$ when $x = 12$ .
$y = -0.76 \times 12 + 26.04$

STEP 5

Perform the multiplication.
$y = -9.12 + 26.04$

STEP 6

Calculate the predicted time spent doing homework for a student who spends 12 hours watching TV.
$y = 26.04 - 9.12$

STEP 7

Complete the subtraction to find the predicted time.
$y = 16.92$
The predicted time spent doing homework for a student who spends 12 hours watching TV is 16.92 hours.

STEP 8

To find the predicted time spent doing homework for a student who doesn't spend any time watching TV, we substitute $x = 0$ into the line of best fit equation.
$y = -0.76x + 26.04$

STEP 9

Now, plug in $x = 0$ into the equation.
$y = -0.76(0) + 26.04$

STEP 10

Calculate the value of $y$ when $x = 0$ .
$y = 0 + 26.04$

STEP 11

Since multiplying by zero gives zero, the predicted time spent doing homework is simply the constant term of the equation.
$y = 26.04$
The predicted time spent doing homework for a student who doesn't spend any time watching TV is 26.04 hours.

STEP 12

To find the predicted decrease in the time spent doing homework for an increase of one hour in the time spent watching TV, we look at the coefficient of $x$ in the line of best fit equation.
$y = -0.76x + 26.04$

STEP 13

The coefficient of $x$ is $-0.76$ , which represents the change in $y$ (time spent doing homework) for each one-unit increase in $x$ (time spent watching TV).

STEP 14

Since the coefficient is negative, it indicates a decrease in the time spent doing homework.
The predicted decrease in the time spent doing homework for an increase of one hour in the time spent watching TV is 0.76 hours.

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.

Studdy Solution

STEP 1

STEP 2

To find the predicted time spent doing homework for a student who spends 12 hours watching TV, we substitute x=12x = 12x=12 into the line of best fit equation.y=−0.76x+26.04y = -0.76x + 26.04y=−0.76x+26.04

STEP 3

Now, plug in x=12x = 12x=12 into the equation.y=−0.76(12)+26.04y = -0.76(12) + 26.04y=−0.76(12)+26.04

STEP 4

Calculate the value of yyy when x=12x = 12x=12.y=−0.76×12+26.04y = -0.76 \times 12 + 26.04y=−0.76×12+26.04

STEP 5

Perform the multiplication.y=−9.12+26.04y = -9.12 + 26.04y=−9.12+26.04

STEP 6

Calculate the predicted time spent doing homework for a student who spends 12 hours watching TV.y=26.04−9.12y = 26.04 - 9.12y=26.04−9.12

STEP 7

Complete the subtraction to find the predicted time.y=16.92y = 16.92y=16.92The predicted time spent doing homework for a student who spends 12 hours watching TV is 16.92 hours.

STEP 8

To find the predicted time spent doing homework for a student who doesn't spend any time watching TV, we substitute x=0x = 0x=0 into the line of best fit equation.y=−0.76x+26.04y = -0.76x + 26.04y=−0.76x+26.04

STEP 9

Now, plug in x=0x = 0x=0 into the equation.y=−0.76(0)+26.04y = -0.76(0) + 26.04y=−0.76(0)+26.04

STEP 10

Calculate the value of yyy when x=0x = 0x=0.y=0+26.04y = 0 + 26.04y=0+26.04

STEP 11

Since multiplying by zero gives zero, the predicted time spent doing homework is simply the constant term of the equation.y=26.04y = 26.04y=26.04The predicted time spent doing homework for a student who doesn't spend any time watching TV is 26.04 hours.

STEP 12

To find the predicted decrease in the time spent doing homework for an increase of one hour in the time spent watching TV, we look at the coefficient of xxx in the line of best fit equation.y=−0.76x+26.04y = -0.76x + 26.04y=−0.76x+26.04

STEP 13

The coefficient of xxx is −0.76-0.76−0.76, which represents the change in yyy (time spent doing homework) for each one-unit increase in xxx (time spent watching TV).

STEP 14

Since the coefficient is negative, it indicates a decrease in the time spent doing homework.The predicted decrease in the time spent doing homework for an increase of one hour in the time spent watching TV is 0.76 hours.

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.

To find the predicted time spent doing homework for a student who spends 12 hours watching TV, we substitute $x = 12$ into the line of best fit equation.
$y = -0.76x + 26.04$

Now, plug in $x = 12$ into the equation.
$y = -0.76(12) + 26.04$

Calculate the value of $y$ when $x = 12$ .
$y = -0.76 \times 12 + 26.04$

Perform the multiplication.
$y = -9.12 + 26.04$

Calculate the predicted time spent doing homework for a student who spends 12 hours watching TV.
$y = 26.04 - 9.12$

Complete the subtraction to find the predicted time.
$y = 16.92$
The predicted time spent doing homework for a student who spends 12 hours watching TV is 16.92 hours.

To find the predicted time spent doing homework for a student who doesn't spend any time watching TV, we substitute $x = 0$ into the line of best fit equation.
$y = -0.76x + 26.04$

Now, plug in $x = 0$ into the equation.
$y = -0.76(0) + 26.04$

Calculate the value of $y$ when $x = 0$ .
$y = 0 + 26.04$

Since multiplying by zero gives zero, the predicted time spent doing homework is simply the constant term of the equation.
$y = 26.04$
The predicted time spent doing homework for a student who doesn't spend any time watching TV is 26.04 hours.

To find the predicted decrease in the time spent doing homework for an increase of one hour in the time spent watching TV, we look at the coefficient of $x$ in the line of best fit equation.
$y = -0.76x + 26.04$

The coefficient of $x$ is $-0.76$ , which represents the change in $y$ (time spent doing homework) for each one-unit increase in $x$ (time spent watching TV).

Since the coefficient is negative, it indicates a decrease in the time spent doing homework.
The predicted decrease in the time spent doing homework for an increase of one hour in the time spent watching TV is 0.76 hours.