Answer:
ŷ = -0.895X + 13.600
Slope = -0.9
Intercept = 13.6
r = - 0.964
Step-by-step explanation:
Given the data:
X- 10.1 9.8 9.7 9.4 8.9 8.7 8.4 8.1
Y- 4.3 4.8 5.3 5.2 5.6 5.8 6.1 6.3
Inputting the data given into the online regression calculator :
The equation of line of best fit :
ŷ = -0.895X + 13.600
Slope = - 0.9(to the nearest tenth)
Intercept = 13.6 (to the nearest tenth)
The correlation Coefficient 'r' of the data supplied is - 0.9643, which implies that a strong negative correlation exists between the dependent and independent variables.
r = - 0.964 (to the nearest thousandth)
Inputting the data into the STAT then Fit Data function of the HP 50g
Graphing Calculator.
The meaning of the strong negative correlation is that the x-values
of the data is decreasing, while the corresponding y-values of the data
increasing.
Reasons:
The least squares regression line equation is the best fit line for the data
The formula for the least squares regression line is [tex]\hat Y = b \cdot X + a[/tex]
Where;
[tex]b = \dfrac{n \cdot \sum X \cdot Y - \left (\sum X \right )\left (\sum Y \right )}{n \cdot \sum X^{2} - \left (\sum X \right )^{2}}[/tex]
[tex]a = \dfrac{\sum Y - b \cdot \sum X}{n}[/tex]
n = The sample size
Inputting the given data into the function Fit Data on a graphing calculator,
by editing ∑DAT.
The left column, represent the x-values, and right column represent the y-
values as follows;
[tex]\begin{array}{|c|cc|} \mathbf{Column \ 1}&&\mathbf{Column \ 2}\\10.1&&4.3\\9.8&&4.8\\9.7&&5.3\\9.4&&5.2\\8.9&&5.6\\8.7&&5.8\\8.4&&6.1\\8.1&&6.3\end{array}\right][/tex]
After inputting the data as above, press enter.
Move the pointer to the Model options line, select choose to choose the
Linear Fit model by selecting OK.
Select OK again for the calculator to do the calculations.
The least squares regression line equation given by the calculator is
presented as follows;
y = 13.5998272884 - 0.894645941278·x
The slope and the y-intercept rounded to the nearest tenth gives;
Correlation coefficient:
The correlation coefficient is given from the data using the following
formula;
[tex]r = \dfrac{n \cdot \sum X \cdot Y - \left (\sum X \right ) \cdot \left (\sum Y \right )}{\sqrt{n \cdot \sum X^{2} - \left (\sum X \right )^{2}\times n \cdot \sum Y^{2} - \left (\sum Y \right )^{2}}}[/tex]
From the graphing calculator, we have the correlation coefficient, given as
follows;
Correlation: (-0.964276229529)
Therefore, to the nearest thousandth;
The high negative value of the correlation coefficient indicates a strong
and near perfect relationship between the variables, x, and y, such that we
have;
Learn more here:
https://brainly.com/question/24848242
