Answer:
Y = 0.4925X - 22.26 ;
(-12.413, 13.398) ;
Yes, there is
Step-by-step explanation:
X = IQ Score ; Y = musical aptitude
The regression equation from the table given using the slope and intercept coefficient :
Y = 0.4925X - 22.26
0.4925 = slope ; Intercept = - 22.26
The 95% confidence interval of the slope :
Confidence interval = b ± Tcritical*SE
Tcritical at 95%, df = n - 2 = (20 - 2) = 18
Tcritical = 2.1009
b = slope Coefficient = 0.4925
S.E = 6.143
Hence, we have :
Confidence interval = 0.4925 ± (2.1009 * 6.143)
Confidence interval = 0.4925 ± 12.9058287
Lower boundary = 0.4925 - 12.9058287 = - 12.413
Upper boundary = 0.4925 + 12.9058287 = 13.398
(-12.413, 13.398)
There is a significant relationship between IQ score and musical aptitude because, 0 is within the confidence interval obtained.
Slope-intercept form:
y=mx+b
m=slope
b=y-intercept
Data of the first line:
m=-5
b=y-intercept=3 (y-intercept=it is the value of "y" when x=0)
y=-5x+3
A line perpendicular to the line y=mx+b will have the following slope:
m`=-1/m
Therefore: the line perpendicular to the line y=-5x+3 will have the following slope:
m´=-1/(-5)=1/5
Point-slope form of a line: we need a point (x₀,y₀) and the slope (m):
y-y₀=m(x-x₀)
We know, the slope (m=1/5) and we have a point (3,2) therefore:
y-y₀=m(x-x₀)
y-2=1/5(x-3) (point-slope form)
y-2=(1/5)x-3/5
y=(1/5)x-3/5+2
y=(1/5)x+7/5 (slope-intercept form)
Answer: the line perpendicular to the first line will be: y=(1/5)x+7/5
Answer is $963.43
Step by step.
The computer is $890. Sales tax is 8.25%.
Multiply $890 x 8.25% (or .0825) and add that tax to the cost.
$890 x 8.25% = 73.43.
$890 + 73.43 = $963.43 is your answer.
Yes it does. If you divide each of the y values by their corresponding x values you will see a pattern. If this pattern is the same number over and over, it is the same ratio.
