The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Age 36 39 48 53 58
Bone Density 358 351 330 325 314
Table

Step 1 of 6 : Find the estimated slope. Round your answer to three decimal places.

-1.973

Step-by-step explanation:

Given the data :

Age 36 39 48 53 58

Bone Density 358 351 330 325 314

Equation of regression line is in the form:

yˆ=b0+b1x

Where y = predicted variable ;

b0 = intercept ; b1 = slope or gradient ; x = predictor variable

Using The correlation Coefficient calculator :

The regression equation obtained is :

ŷ = -1.97316X + 427.94399

From the equation ;

The slope or gradient (b1) = - 1.97316

Hence, estimated slope to 3 decimal places is : - 1.973

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺