The table below gives the number of hours seven randomly selected students spent studying and their corresponding midterm exam grades. using this data, consider the equation of the regression line, yˆ = b0 + b1x, for predicting the midterm exam grade that a student will earn based on the number of hours spent studying. keep in mind, the correlation coefficient may or may not be statistically significant for the data given. remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

hours studying midterm grades
1.5 67
2.5 69
3 80
3.5 81
4 86
4.5 89
5.5 94

step 1 of 6: find the estimated slope. round your answer to three decimal places.

step 2 of 6: find the estimated y-intercept. round your answer to three decimal places.

step 3 of 6: determine the value of the dependent variable yˆ at x = 0.

step 4 of 6: determine if the statement "not all points predicted by the linear model fall on the same line" is true or false.

step 5 of 6: find the estimated value of y when x = 4.5. round your answer to three decimal places.

step 6 of 6: find the value of the coefficient of determination. round your answer to three decimal places

1)

2)

3)

4) False. The values predited will fall on the same line since we are estimating  the values with just one line.

5)

6)

And that means that the linear model explains 94.29% of the variation.

Step-by-step explanation:

We assume that the data is this one:

x:1.5,2.5, 3, 3.5 , 4, 4.5 ,5.5

y: 67, 69, 80, 81, 86, 89, 94.

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

For this case we need to calculate the slope with the following formula:

Where:

So we can find the sums like this:

With these we can find the sums:

And the slope would be:

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Now we can find the means for x and y like this:

And we can find the intercept using this:

So the line would be given by:

Step 3 of 6: Determine the value of the dependent variable yˆ at x = 0.

Step 4 of 6: Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.

False. The values predited will fall on the same line since we are estimating  the values with just one line.

Step 5 of 6: Find the estimated value of y when x = 4.5. Round your answer to three decimal places.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places

n=7  

And in order to calculate the correlation coefficient we can use this formula:

And the determination coeffcient is just the square of the correlation coefficient given by:

And that means that the linear model explains 94.3% of the variation.