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Alenkasestr [34]
3 years ago
8

Use the given data to find the equation of the regression line. examine the scatterplot and identify a characteristic of the dat

a that is ignored by the regression line. x 1212 1313 66 55 1010 1111 77 99 33 88 44 y 20.2120.21 20.2320.23 13.1913.19 10.8710.87 19.1919.19 19.8719.87 15.1815.18 18.1818.18 5.235.23 16.8516.85 8.218.21 modifyingabove y with caretyequals

Mathematics
1 answer:
kari74 [83]3 years ago
7 0

Answer:

y = 1.5x + 3.2009  

Step-by-step explanation:

I plotted your points and drew a linear regression line.

Its equation is

y = 1.5x + 3.2009

The regression line ignores the fact that the points fall along a smooth curve.

A parabolic regression line fits the data much better.

The equation for that line is

y = - 0.1647x² + 4.1357x - 5.6946

It is the equation for a vertical parabola opening downward.

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The diameter of steel rods manufactured on two different extrusion machines is being investigated. Two random samples of sizes
devlian [24]

Answer:

(a) There is no evidence to support the claim that the two machines produce rods with different mean diameters.

P-value is 0.818

(b) 95% confidence interval for the difference in mean rod diameter is (-0.17, 0.27).

This interval shows that the difference in mean is between -0.17 and 0.27.

Step-by-step explanation:

(a) Null hypothesis: The two machines produce rods with the same mean diameter.

Alternate hypothesis: The two machines produce rods with different mean diameter.

Machine 1

mean = 8.73

variance = 0.35

n1 = 15

Machine 2

mean = 8.68

variance = 0.4

n2 = 17

pooled variance = [(15-1)0.35 + (17-1)0.4] ÷ (15+17-2) = 11.3 ÷ 30 = 0.38

Test statistic (t) = (8.73 - 8.68) ÷ sqrt[0.38(1/15 + 1/17)] = 0.05 ÷ 0.218 = 0.23

degree of freedom = n1+n2-2 = 15+17-2 = 30

Significance level = 0.05 = 5%

Critical values corresponding to 30 degrees of freedom and 5% significance level are -2.042 and 2.042.

Conclusion:

Fail to reject the null hypothesis because the test statistic 0.23 falls within the region bounded by the critical values -2.042 and 2.042.

There is no evidence to support the claim that the two machines produce rods with different mean diameters.

Cumulative area of test statistic is 0.5910

The test is a two-tailed test.

P-value = 2(1 - 0.5910) = 2×0.409 = 0.818

(b) Difference in mean = 8.73 - 8.68 = 0.05

pooled sd = sqrt(pooled variance) = sqrt(0.38) = 0.62

Critical value (t) = 2.042

E = t×pooled sd/√n1+n2 = 2.042×0.62/√15+17 = 0.22

Lower limit of difference in mean = 0.05 - 0.22 = -0.17

Upper limit of difference in mean = 0.05 + 0.22 = 0.27

95% confidence interval for the difference in mean rod diameter is between a lower limit of -0.17 and an upper limit of 0.27.

3 0
3 years ago
After school, Camille had a science club meeting for 1 hour, followed by a choir rehearsal that lasted for 40 minutes. If Camill
Vedmedyk [2.9K]
It would be 3:40 since 1 hour and the 40 minutes add up and the choir is after the meeting
7 0
3 years ago
Read 2 more answers
The accompanying table shows the number of bacteria present in a certain culture over a 4 hour period, where x is the time, in h
Vlad [161]

Answer:

Step-by-step explanation:

I really hope you know how to use your calculator to find regression equations, because in this forum it is impossible to teach you how to do that. I ran the data through my calculator and got the exponential equation as

y=1963.56(1.14)^x which means at 4 hours, we started with 1963 bacteria and it is growing at a rate of 114% each hour. Since we started out with an x value of 0, and that value represents the number of bacteria after 4 hours, then time 0 is 4 hours, which means that time 12 is 16 hours. We replace the x in the equation with a 12 and do the math:

y=1963.56(1.14)^{12 which gives us, in the end,

y = 9460

4 0
3 years ago
What value of x makes the equation 5(7x-3)-x=-4x-(-9-2x) true? please help :)
stiv31 [10]
X = 2/3 makes the equation true.

Answer: x = 2/3
7 0
3 years ago
Find the distance between the points (6,5√5) and (4,3√2).<br> 2, 2√2, 2√3
FromTheMoon [43]

Answer:

D=\sqrt{(147-30\sqrt{10}}

Step-by-step explanation:

Here we are required to find the distance between two coordinates. We will use the distance formula to find the distance

The distance formula is given as

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Here we are given two coordinates as

(6,5\sqrt{5} ) , (4,3\sqrt{2} )

Substituting these values in the Distance formula given above we get

D=\sqrt{(6-4)^2+(5\sqrt{5} -3\sqrt{2}) ^2}

D=\sqrt{(2)^2+(5\sqrt{5})^2+(3\sqrt{2})^2-2*5\sqrt{5}*3\sqrt{2}}\\

D=\sqrt{4+125+18-2*15\sqrt{10}}\\D=\sqrt{147-30\sqrt{10}}\\

Hence this is our answer

6 0
3 years ago
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