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3 years ago

Consider the following data points.

Mathematics

2 answers:

Hoochie [10]3 years ago

8 0

Answer:

the equation of the least-squares line for the data is: $\hat Y=9.3+1.3x$

Step-by-step explanation:

In a simple linear regression model, such as, $\hat Y=b_0+b_1x$ , the coefficients bo and b1 are estimated through the method of least squares by the use of the equations:

$b_1=\frac{S{xy}}{S_x^2}\\\\b_0=\bar{y}+b_1 \bar{x}$

For the data provided you have to:

$S_{xy}=\frac{\sum {(x_i-\bar x)(y_i-\bar y)}}{n-1}=3.25\\\\S_x^2=\frac{\sum {(x_i-\bar x)^2}}{n-1}=2.5\\\\\bar y=5.4$ , thus:

$b_1=\frac{3.25}{2,5}=1.3\\\\b_0=5.4+1.3(3.0)=9.3$

the equation of the least-squares line for the data is:

$Y=9.3+1.3x$

Naddika [18.5K]3 years ago

3 0

Answer:

y= 9.3 1.3

Step-by-step explanation:

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Some of Mrs. Turay’s eighth graders took the PSAT test. Score totals of ten of her students are below. Calculate the mean and th

den301095 [7]

Answer:

(a) Mean=74

(b) Median=70

Step-by-step explanation:

We have been given a data set of PSAT scores of Mrs. Turay's eight graders. We are asked to find mean and median of the given data set.

(a) Let us find mean of data set by dividing the sum of given scores by the number of students.

$\text{Mean}=\frac{60+62+67+69+70+70+71+75+76+120}{10}$

$\text{Mean}=\frac{740}{10}=74$

Therefore, the mean test score will be 74.

(b) Now let us find median of our given data set. We have been given that number of students is 10, therefore, our median will be the average of 5th and 6th term.

60, 62, 67, 69, 70, 70, 71, 75, 76, 120.

We can see that 5th term is 70 and 6th term is 70 as well.

$\text{Median}=\frac{70+70}{2}$

$\text{Median}=\frac{140}{2}$

$\text{Median}=70$

Therefore, the median test scores will be 70.

(c) We can see that our data set has an outlier score as 120, which has increased the mean. Mean score is greater than median score. Since median is not affected by extreme value outliers, therefore, median will be the best measure of center for given test scores.

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3 years ago

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bixtya [17]

Answer:

Step-by-step explanation:

4). This is an exponential function.

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