To graph: The scatter plot of the data.
Consider the Noise level in decibel as the x coordinates and the M.R.T score as the y coordinates.
The scatter plots of the given data are shown below in Figure 1.
From Figure 1, all the points are plotted on the graph. No two points coincide each other.
To find: The regression line that represents the given data and draw the graph for it.
The regression that represents the given data is .
By the use of online calculator, the regression line for the given data obtained is , where M.R.T score is the y-intercept and noise level is the x-intercept.
The above regression line is in the form of linear equation.
Therefore, the linear function that represents the given data is .
The graph that represents the equation is shown below in Figure 1.
From Figure 2, the graph for the linear equation is a straight line.
To find: The correlation coefficient and to check whether the linear model appropriate or not.
The correlation coefficient is .
The formula for the correlation coefficient is .
Compute the values of the summation of x, y, xy, , and are shown in below table.
It is observed that the value of n = 7.
Substitute the values that are obtained in the table to compute the correlation coefficient by using the above mentioned formula.
On further simplification.
Thus, the value of the correlation coefficient is .
To find: The estimate value of the intelligibility of a sentence at a 94-dB.
The estimate value of the intelligibility of a sentence at a 94-dB is 52.912 %.
Consider the noise level at 94-dB.
From part (b), it is obtained that the linear equation that represents the given data is .
Substitute x = 94 in the above equation to compute the M.R.T score.
Thus, the estimate value of the intelligibility of a sentence at a 94-dB is 52.912 %.
Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!