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Aleonysh [2.5K]
2 years ago
5

Find the equation of the least squares regression line. Show all calculations, and be sure to define any variables used.

Mathematics
1 answer:
spayn [35]2 years ago
3 0
Steps
Step 1: For each (x,y) point calculate x2 and xy.
Step 2: Sum all x, y, x2 and xy, which gives us Σx, Σy, Σx2 and Σxy (Σ means "sum up")
Step 3: Calculate Slope m:
m = N Σ(xy) − Σx Σy N Σ(x2) − (Σx)2
Step 4: Calculate Intercept b:
b = Σy − m Σx N.
Step 5: Assemble the equation of a line.
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Use the Remainder Theorem to completely factor p(x) = x ^3 + 7x ^2 + 11x + 5.
tigry1 [53]

In order to use the remainder theorem, you need to have some idea what to divide by. The rational root theorem tells you rational roots will be from the list derived from the factors of the constant term, {±1, ±5}. When we compare coefficients of odd power terms to those of even power terms, we find their sums are equal, which means -1 is a root and (x +1) is a factor.

Dividing that from the cubic, we get a quotient of x² +6x +5 (and a remainder of zero). We recognize that 6 is the sum of the factors 1 and 5 of the constant term 5, so the factorization is

... = (x +1)(x +1)(x +5)

... = (x +1)²(x +5)

_____

The product of factors (x +a)(x +b) will be x² + (a+b)x + ab. That is, the factorization can be found by looking for factors of the constant term (ab) that add to give the coefficient of the linear term (a+b). The numbers found can be put directly into the binomial factors to make (x+a)(x+b).

When we have 1·5 = 5 and 1+5 = 6, we know the factorization of x²+6x+5 is (x+1)(x+5).

4 0
3 years ago
Read 2 more answers
Scientific notation for 7×10^9​
Alex17521 [72]

Answer:

7,000,000,000

Step-by-step explanation:

7×10^9

The number after ten is how many zeros you put.

5 0
2 years ago
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Write the slope-intercept form of the equation for the line.
Fantom [35]
Well, let's take a peek at the graph of that line, hmmm let's pick two points, heck, those tow on the extremes anyway, and those are (-5,2) and (5,-1), alrite.. now, let's do some checking on that.

\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%   (a,b)
&({{ -5}}\quad ,&{{ 2}})\quad 
%   (c,d)
&({{ 5}}\quad ,&{{ -1}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-1-2}{5-(-5)}\implies \cfrac{-1-2}{5+5}
\\\\\\
\cfrac{-3}{10}

\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=-\cfrac{3}{10}[x-(-5)]
\\\\\\
y-2=-\cfrac{3}{10}(x+5)\implies y-2=-\cfrac{3}{10}x-\cfrac{3}{2}\implies y=-\cfrac{3}{10}x-\cfrac{3}{2}+2
\\\\\\
y=-\cfrac{3}{10}x+\cfrac{1}{2}
5 0
3 years ago
What is 1.2+d+0.4=9.7?
Cloud [144]
1.2 + d + 0.4 = 9.7

1.6 + d = 9.7

1.6 (-1.6) + d = 9.7 (-1.6)

d = 8.1

your answer is 8.1

hope this helps
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3 years ago
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A paperback book company chargers $6 for each paperback book plus $4 for shipping and handling per order. What would be the tota
Andrews [41]
$6(3)+4= $18+$4= $22
7 0
3 years ago
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