$r=0.77$ , $\hat{y}=770.50+39.37x$ and volume of cerebral brey matter for a child whose head circumference Z score at age 12 months was 1.9 is $\hat {y}=920.10$

Step-by-step explanation:

We attached a table below,

$(a)$ We attached a table below,

Therefore ,

correlation coefficient $r=\frac{\frac{1}{18}(21766.7)-(\frac{27.25}{18} )(\frac{13890}{18} ) }{\sqrt{\frac{1}{18} (59.8435)-(\frac{27.25}{18} )^2}\sqrt{\frac{1}{18}(10767400)-(\frac{13890}{18} )^2 } }$

$=\frac{41.04}{53.19}$

$=0.77$

$(b)$ We calculate the least squares equation.

$b_1=r(\frac{\sigma_y}{\sigma_x} )\\ =(0.77)(\frac{\sqrt{\frac{1}{18} (10767400)-(\frac{13890}{18} )^2} }{\sqrt{\frac{1}{18}(59.8435)-(\frac{27.25}{18} )^2 } } )\\ =0.77(\frac{52.15}{1.02} )\\ =0.77(51.13)\\ =39.37$

Now , calculate intercept coefficient.

$b_0=\bar{y}-r\bar{x}\\$

$=(\frac{\sum{y}}{n} )-0.77(\frac{\sum{x}}{n} )\\=(\frac{13890}{18} )-0.77(\frac{27.25}{18} )\\=771.67-1.17\\=770.50$

Therefore, the regression equation is, $\hat{y}=770.50+39.37x$

$(c)$ Find the volume of cerebral brey matter for a child whose head circumference Z score at age 12 months was 1.8

$\hat{y}=770.50+39.37x$

$=770.50+39.37(1.9)\\=770.50+74.80\\=920.10$

5 0

2 years ago

Tracy needs to find the length & width of the equipment storage room where she works. The room is 4 meters longer than it is

AveGali [126]

Answer:

length = 8m

width = 4m

Step-by-step explanation:

The perimeter of a rectangle is the formula: P = 2w + 2l, where 'w' is equal to the width and 'l' is equal to the length. In this case, the width can be expressed as 'w' and the length, which is '4 meters longer than its width' would be 'w +4'. So, when you put these expressions into the equation:

P = 2w + 2(w +4)

P = 2w + 2w + 8 or 4w + 8

Since perimeter = 24m, plug it in and solve for 'w':

24 = 4w + 8

Subtract 8 from both sides: 24 - 8 = 4w + 8 - 8 or 16 = 4w

Solve for w: w = 4m

Solve for l: l = w + 4 or 4+4, so l = 8m

7 0

2 years ago