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3 years ago

PLEASE HELP I WILL REWARD BRAINLIEST

Mathematics

1 answer:

RUDIKE [14]3 years ago

5 0

35,23,32,25,27,31,29,30
1st: Order data from smaller to greater: 23,25,27,29,30,31,32,35

2nd Find the median of the set (central value). Since the number of data is even, then the median is the average between 29 & 30 = (29+30)/2 =29.5,(we will not use the median value, just for indication)

3rd, Find the central value of the subset on the left of 29 (that is 23,25,27)
This lower median =25 . This is called Q1
4th , Do the same with the subset on the right of 30 (that is 31,32,35).
This higher median = 32 is called Q3 (for your info the 1st median=29.5 is Q2)
The IQR or inter quartile range is Q3 - Q1 (or upper - lower Q)
IQR = 32-25) =7

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Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 4:

The line of regression is $\hat y = a+bx$ where:

$a=\overline y-b \overline x$

$b=\frac{r*s_y}{s_x}$

We are given that $\overline y=75$ , $s_y=8$ , $\overline x=280$ , $s_x=30$ , and $r=0.60$ , therefore our slope, $b$ , is:

$b=\frac{r*s_y}{s_x}$

$b=\frac{(0.60)(8)}{30}$

$b=0.16$

Therefore, the slope of the regression line is 0.16, which can be used along with the values of $\overline y$ and $\overline x$ to find the constant $a$ :

$a=\overline y-b \overline x$

$a=75-(0.16)(280)$

$a=30.2$

This means our final regression line is $\hat y = 30.2 + 0.16x$

Problem 5:

The slope, $b=0.16$ , means that for every 1 point earned for a student's pre-exam total, their final exam score will increase by 0.16 points for each point they earned on the pre-exam.

Problem 6:

The y-intercept (or constant), $a=30.2$ , means that if a student's pre-exam total were 0, then they would expect to get a 30.2 on the final exam.

Problem 7:

$R^{2}=(0.60)^{2}=0.36=36\%$

Problem 8:

The fraction of variability (aka. coefficient of determination), $R^2$ , means that a certain proportion (or percentage) of the variance in the response variable can be explained by the explanatory variable. In context, this means that 36% of the variance in final exam scores can be explained by the pre-exam scores.