# Mathematics

8) The following data represent the heights and weights of various baseball players. (in inches/ pounds)

Player Height, x Weight, y Player Height, x Weight, y

Nate 72 197 Greg 70 195

Derek 71 201 Randy 77 240

Mark 73 192 Josh 71 193

Jon 74 209 Pat 74 203

(a) Compute the least-square regression line. Ŷ=(…..)x- (……)(Do not round until the final answer, then round to three decimal places as needed)

(b) Remove the value corresponding to Randy and compute the least square regression line the correlation coefficient.

(c) Do you thing that Randy is an influential observation.

9) The time it takes for a planet to complete its orbit around a particular star is called the planet’s sidereal year.The sidereal year of the planet is related to the distance the planet is from the star. Accompanying data show the distance of the planets from a particular star and their sidereal years. Complete part a through e. x million of miles/ y sidereal year

Planet Distance from the star x Sidereal Year, y

Planet1 36 0.22

Planet2 67 0.64

Planet3 93 1.00

Planet4 142 1.88

Planet5 483 11.9

Planet6 887 29.3

Planet7 1,785 84.0

Planet8 2,797 165.0

Planet9 3.675 248.0

(a) Has been done.

(b) Determine the correlation between distance and sidereal year. The correlation between distance and sidereal year is (……)(Round to three decimal places as needed).

(c) Compute the least square regression line.

(d) Plot the residuals against the distance from the star

(e) Do you think the least squares regression line is good model?

1) For the data set shown below, do they following. (a) Compute the standard error the point estimate for σ. (b) Assuming the residuals are normally distributed, determine Sb1. (c) Assuming the residuals are normally distributed, test H0;β1=0 versus H1; β1≠0 at the a=0.05 level of significance. The null hypothesis is that x and y are not linearly related.

X 3 4 5 7 8

Y 5 6 8 13 15

a) Determine the point estimate for σ. Se ≈ (…….)(Do not round until the final answer. Then round to four decimal places as needed)

b) Recall that b1 is the estimate of slope of the regression line β1. The sample standard error of b1 is given by the following formula.

c) In order to conduct the hypothesis test, first calculate the test statistic t0.(Explain the result; rejected or do not reject; do the relation exists between x and y?).

2) For the data set shown below, do they following. (a) Compute the standard error the point estimate for σ. (b) Assuming the residuals are normally distributed, determine Sb1. (c) Assuming the residuals are normally distributed, test H0;β1=0 versus H1; β1≠0 at the a=0.05 level of significance.

X 20 30 40 50 60

Y 98 95 91 81 68

a) Determine the point estimate for σ. Se = (…….)(Do not round until the final answer. Then round to four decimal places as needed)

b) Assuming the residuals are normally distributed, determine Sb1.

c) In order to conduct the hypothesis test, first calculate the test statistic t0.(Explain the result; rejected or do not reject; do the relation exists between x and y?).

3) A concrete cures it gains strength. The following data represent 7 days and 28 day strength in pounds per square inch (psi) of a certain type of concrete.

7 day strength psi, x 3330 2620 3380 2300 2480

28 day strength psi, y 4850 4190 5020 4070 4120

a) Compute the standard error of the estimate, Se. Se≈(……) (Do not round until the final answer, Then round to four decimal places as needed)

b) Determine whether the residuals are normally distributes

c) If the residuals are normally distributed, determine Sb1

d) If the residuals are normally distributed, test whether a linear relation exists between 7 day strength and 28 day strength a= 0.05 level of significance.

e) If the residuals are normally distributed construct a 95% confidence interval about the slop of the true least squares regression line.

f) What is the estimate mean 28 day strength of this concrete if the 7 day is 3000 psi?

4) Supposed a multiple regression model is given by ŷ= -3.98×1 – 9.03×2 – 37.73. What would an interception of the coefficient of x1 be? Fill in the blank below

An interception of the coefficient of x1 would be “if x1 increases by 1 unit, then the response variable will decrease by (……) units, on average, while holdingx2 constant.”

5) The regression equation ŷ = 56,777.848 + 4401.106x – 46.38 describe the median income, y, at different ages, x, for residents of a certain country. Complete parts (a) through (c)

(a) And (b) have been done

(c)How much does median income change from 40 to 50 years of age?

The median income (Increases / decreases) by $(……..) from 40 to 50 of age (Round to the nearest cent as needed)

6) Researchers develop a model to predict the age, y, of the individual based on the gender of the individual ,x1 (0=female, 1= male), the height of the second premolar, x2, the number of teeth with root development, x3, and sum of the normalized heights of seven teeth on the left side of the month, x4. The normalized height of the seven teeth was found by dividing the distance between teeth by the height of the tooth. Their model is shown below. Complete parts (a) through (d).

Ŷ= 9.139 + 0.392×1 + 1.256×2 + 0.678×3 – 0.90×4 – 0.174x3x4

(a) Based on this model, what is the expected age of a female with x2 = 27mm, x3=9, and x4= 16mm? (………) years.( Round to one decimal place as needed)

(b) Based on this model, what is the expected of a male with x2=27, x3=9 and x4=16mm

(c) What is the interaction term? What variable interact?

(d) The Coefficient of determination for this model is 85.5%. Explain what this means.

7) Determine if there is a linear relation among air temperature x1, wind speed x2, and wind child y. The following data show the measurement value for various days.

X1 -10 30 0 -30 20 0 30 30 -20 -30 -30 -20 10 -10

X2 50 30 10 100 90 40 20 50 30 50 70 40 80 20

Y -62 0 -22 -104 -32 -44 6 -8 -64 – 88 -98 -70 -44 -44

(a) Find the least squares regression equation Ŷ= b0 + b1x1 + b2x2, where x1 is air temperature and x2 is wind speed, and y is the respond variable, wind chill.

Ŷ= (……) + (…….)x1 + (…….)x2 (Round to three decimal places as needed).

(b) Draw residual plots to assess the adequacy of the model. (Create a residual plot for air temperature and for wind speed).

What might you conclude based on the plot of residuals against wind speet.