# statistics hmwrk

**QUESTION 1.**

**(a**). A biologist assumes that there is a direct alliance betwixt the equality of fertilizer arranged to tomato insert and the later succumb of tomatoes obtained. Eight(8) tomato inserts of the identical multiformity, were selected at purposeless and treated, weekly, after a while a disintegration in which x grams(g) of fertilizer was dissolved in a urban bulk of breathe-into. The succumb y kilograms (kg) of tomatoes was narrative as follows.

Plant

A

B

C

D

E

F

G

H

x

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

y

3.9

4.4

5.8

6.6

7.0

7.1

7.3

7.7

(i). Plot a scatterplot of succumb, y opposite equality of fertilizer, x. **( 3 aims)**

(ii). Calculate the equation of the last balance retreat course of y on x. **( 8 aims)**

(iii). Consider the succumb of a insert treated, weekly, after a while a 3.2 grams of fertilizer.

**( 2 aims)**

(iv). Indicate why it may not be expend to use your equation to forebode the succumb of a insert treated weekly after a while 20 grams of fertilizer. **( 2 aims)**

(b). The board under shows a Verbal Reasoning experience scores, x and an English experience scores, y for each of a purposeless illustration of view (8) effect who took twain experiences

Child

A

B

C

D

E

F

G

H

x

112

113

110

113

112

114

109

113

y

69

65

75

70

70

75

68

76

(i). Calculate the consider of the issue twinkling apposition coefficient betwixt the scores in Verbal Reasoning and English. **( 8 aims) **

(ii).Comment briefly, in texture on the fruit obtained in disunite(i). **( 2 aims)**

**QUESTION 2.**

**(a).**(i).Suppose that the shiftings X and Y meet the four assumptions for retreat inferences such that for illustrations of bigness n, each after a while the identical considers X_{1}, X_{2}, X_{3}…………………… X_{n}, for the forebodeor shifting, List the three properties that must repose for the emerge b1 of the illustration retreat course.

(ii).What dispensation is used for the inferences for β_{1} **(2 aim).**

(iii).In a supposition experience for the emerge β_{1} such that Ho:β_{1}=0 vs. Ha:β_{1}≠0, transcribe the formula for the experience statistic and recite its degrees of immunity. **(2 aim). **

**(b)**.When you are asked to use the hazardous consider adit to pass a Retreat t-experience recite the aftercited.

(i).Purpose **(2 aim).**

(ii).Assumptions **(2 aim). **

(iii).All the six steps **(7 aims) **required to strengthen you to entire such a experience.

**(c). **Consider the aftercited basis on the age and worth for a illustration of eleven (11) Honda cars as displayed under.

Age(yr) x

5

4

6

5

5

5

6

6

2

7

7

Price($100) y

85

103

70

82

89

98

66

95

169

70

48

At a 5% consciousness smooth, do the basis arrange satisfactory indication to infer that age is adapted as a direct forebodeor of worth for the cars? .Use the hazardous consider adit for your experience.

**[Hint:** Retreat equation is y_{hat}=195.47-20.26x, and Standard untruth of the consider Se=12.58**]** **(10 aims).**

**QUESTION 3.**

The aftercited are the age and worth (thousands of dollars) basis for Corvettes from a car dealership in Sterling, Virginia. Meet steadfast the DDXL output of the basis from retreat dissection.

x(Age)

6 6 6 2 2 5 4 5 1 4

y(Price)

290 280 295 425 384 315 355 328 425 325

*Dependent shifting is y and fractions shifting is x.*

*No Selector, 10 entirety cases.*

*R ^{2}=93.7% R^{2} (adjusted)=92.9%*

*S=14.25 after a while 10-2=8 degrees of immunity*

*Source Sum of Squares df Mean Square F-ratio*

*Regression 24057.9 1 24057.9 119*

*Residual 1623.71 8 202.964 *

*Variable Coefficient s.e of Coeff t-ratio prob*

*Constant 456.602 11.43 39.9 <0.0001*

*X -27.9029 2.56 -10.9 <0.0001*

* *

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**(a).(i).** From the DDXL output transcribe the retreat equation. **(2 aims)**

(ii).From the DDXL output, metaphor out the consider of S_{e}. **(1 aim)**

(iii). Calculate the consider of S_{xx} from the basisby using the considers of x. **(5 aims).**

**(b).**Obtain a 90% trust period for the moderation worth of all 3-year old cars by using the subject moderation t-period process on page#17 & page#18 of minority E collocate disquisition notes.**[**By using the considers of S_{e} from (a)-(ii) and S_{xx} from(a)-(iii), you can meet (b)**] (7 aims)**

** (c).**Obtain a 90% forebodeion period for the worth of a 3-year old car by using the forebodeed consider t-period process on page#20 & page#21 of minority E collocate disquisition notes. .**[**By using the considers of S_{e} from (a)-(ii) and S_{xx} from(a)-(iii), you can meet (c)**] (7 aims)**

**(d). **By comparing your fruits from (b) and (c) which period is depart? and present two reasons why such fruits is expected. **(3 aims)**