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introduces a data set on birth weight of babies. Another variable we consider is parity, which is 0 if the child is the first born, and 1 otherwise. The summary table below shows the results of a linear regression model for predicting the average birth weight of babies, measured in ounces, from parity.$$\begin{array}{rrrrr}\hline & \text { Estimate } & \text { Std. Error } & \text { t value } & \operatorname{Pr}(>|\mathrm{t}|) \\\hline \text { (Intercept) } & 120.07 & 0.60 & 199.94 & 0.0000 \\\text { parity } & -1.93 & 1.19 & -1.62 & 0.1052 \\\hline\end{array}$$(a) Write the equation of the regression line.(b) Interpret the slope in this context, and calculate the predicted birth weight of first borns and others.(c) Is there a statistically significant relationship between the average birth weight and parity?

Intro Stats / AP Statistics

Chapter 6

Multiple and logistic regression

Linear Regression and Correlation

Temple University

Cairn University

Oregon State University

Boston College

Lectures

0:00

27:59

The following data represe…

02:38

Using the data in the Stud…

01:22

Vahya infant weights A stu…

04:52

Weight of Children A numbe…

03:08

Growth of a baby. The medi…

others. Once we are given the following data represent a distribution of worth beds in ground for babies. Invisible pregnancy. Well, full form this 37 to 41 weeks table is given in the question. So we need to find A B C D. Up to half. Right. And we need to answer these explainers. Alright, so let us start with a part a part is. So basically if I write for this, so basically we need to first calculate our considered relative frequency distribution can. Right? So basically relative frequency, relative frequency distribution table. We need to draw distribution table. We need to draw first for this. We need to find what is relative frequency, relative frequency is a frequency of particular subgroup, frequency of service, subgroup divided by total frequency. Right? Total frequency values some of all frequencies. Right. So basically total number. Right? So total frequency. Right? Total frequency. Now now let us draw our table. What would be my table of that. So if I calculate or draw the table, it would be something like that. And this will come out as something like that. Right? So basically a big table we have to draw and this is the outliers of that table. And to hear what we will show is are we will divide that table and we will definitely solve it. So this first column represents. So this this represent worth the wait, if I write this representative worth the wait. Right. And this is in grams. And this is number of live births right now let us fill all the table. Rights of 402499 here and here. 500 to 999. And here 9000 to 14 99. And this is basically 1500 to 1999 and more. I can right here. This is 2002 to 4 double line. And this is 2500 to 2500 to two triple line. And this is basically 2349 3009. And this is basically 3500 to 3999. Right? And the next if I can ride this is 4002 to 4499. And this is 4500 to 4 triple line. And this is 25 5004 double line. Right Now let us talk about the frequencies for each and every data group. This is 201 1645 and this is 93659219192191 and 56 and 9319. And this is 1387335. Next from would be nine double eight and 0112 double 57 double zero and 36 766 and 3994. Right now we need to calculate the summer frequency roughly. We have calculated death. All the values is 3353 double it for rights. So this is basically summer frequency. Now we need to calculate our relative frequency. So we will calculate that. So what would be my answers? Our letters calculate our relative frequency. To solve our first question, our relative fish frequency table. Right. So basically this is 22 divided by total frequency. So after roughly calculation this is 65778. Multiplied by 10 raised to power minus six. Right? And if I write for 201 divided by total, this is six double 0978 multiply by 10 days to power minus five. Right? Or it can be a tennis or 50.0. So this is four end of two. So pointed double 06 5778. Right? Or if I write for this, these are these are 12345 and minus five. So basically if I write for them but here five zeroes will come right, five zeroes will come. So five if I write for it, so 50.0 and this is zero and 657. Right? And here also if I write for this 6570.0 point 0000 and this is six and this is double 09, double 09. Now next time would be if I write roughly pointed double zero sorry, pointed triple 044918. Right? Now, this this value would be if I if I calculate point double zero pointed double 028 and double 079. This is 790.27564. And this value would be point of 170 double triple 2951. And this value would be if I talk about the next value, this is point 41480804806. And this is 29510.0.295409 double 36. And this is point 076452759. And the next value is 764527590.10 double nine. And the next value would be pointed double zero double 194. Right, So these are roughly calculated. I have written So this this we have got our relative frequency table. Right now, let us talk about relative frequency instagram, relative frequency hissed a gram. We need to find frequency hissed a gram. Now, if I write for the instagram, so this is our we need to find for it. If I if I draw it, so let's let's start from the very right side. So to make it clear, so if I draw for this, so let's make it Right. So it was started, it is started from here and this must be something like this. Right? So if I calculate this must be 0.1, this is 0.2, this is 0.3, this is 0.4 and this is basically 0.5. Right, distributed. And this is the this is the distribution for relative frequency, relative frequency shown from here and this shown as x is so X in the it's the birth weight worth of weight worth waiting grams worth of weight subgroups, waiter subgroups, ingram's right? So basically, if I write for this, if I break all, so this will be breaking something like this. So 0 to 500. So basically 500,000 and 1500. This is 2000 And 2500 and 3000. Right? 3500. Right now let's check. Other 3500. And this is basically again 4000 right? 4000? And we need to increase that further. We need to increase that further. So this I will increase something like this. Right now we are going to calculate the next. So this 4000 now 4500 and 5000 right? 4500. So this is basically 454,500. And this is basically 5000, right? We will start by drawing this 3000 to 3500 which is exceeding 35000.4. So it will be something like this. If I draw for this lex luthor, lex store. So we will have to start from this and this will go beyond 0.4 Right under we will write the exact value and this will go also something like this. Now, now this this bar must be connected. Right? This bar must be connected. So we can write this as this is this is for 3000 to 3500.414 point 41 fortify Right? For this 410.414 value. Right? Basically exciting to this. Now let us calculate for other values. So we have calculated for this. Now come to this value. This value must be and this value so 0.17 it is so 2500 to 3000.17 25 100 to 3000.170 point 17 would be something here. Right? So let us draw it for this. Up to this, Up to death with the right, Let us draw this right? Now, if I cover this is 0.414 and this is 0.170 to right 0.1702. Now next 35 to 3500 to 4000 which is 40000.295 point 295 basically covering to this, right? So basically if I write for this, this is basically if I write This is .295. Now covering this. So So it will cover something like this. Right? So if I write for this, this this .295 or something. Now let's calculate for others, draw for others. And this is covered, this is covered and this is covered. Now come to other parts oh this is this is 0.76 which is highest amongst the left. So if I draw this, this will be something like 4000 to 44 99 44 99. 4000 to 40 for 9 99. So this is Equal into equal in 2.07 right? So this is basically .1. So .7 will be there. But this is basically .07. So this is very small. Leftovers are very small. So we need to take assumptions here to draw them correctly. So this is basically pointed 076. So very less. So if I draw this, select suppose I have drawn uh something to this extent, Right? But very small. Right? So we can't predict exactly. So if I come to this this part this is 4500-4 triple line. So this is smaller than this .07. So we can write this is this is smaller than this. Right? So this must speak about something like this right Now if I draw five pencils that would be better. And this 5000 to 4500 to 5000. This is very small. This is very small. And we can draw this by Right? Very small. So if I write something this would be better. So .076. Right and different would be .01.01 zero double 9.11 would be better and appointed double zero point double 011, right 11. And this is nine. So basically can be written as to now what are the left water leftovers? So this is okay, this is okay Now we have left with the with the death values too. So let us start with this value because this is very the sorry this is this is start with this value because this is the biggest amongst this, this and this is .0-7. So if I write for this, uh if I draw for this uh as assumption. So basically if I assume this would be smaller than this and this is very small right? This is very small. As I have seen why this is very small. So because this this has some double zero points. Uh this this is very small than this, this 00.2 double zero and this has three zeros. So this is smaller than this, right? This is 30. So smaller than this. So if I draw this is very small than this right now let us come to other values. So this is triple 06 double 09 and this is 659. So this is greater. And this is small. So if I draw draw for it. So if I consider this is something like this and this is something like this. Right? So if I put all the values, all the values would be this is 0.0 to seven. This is 70.27 and this is pointed double zero double zero. You wait right pointed double 028 and upper value would be upper value would be pointed triple 04 pointed triple 04. And if I talk about the other values which are which are point for four times zero and six. Right 60.4 times zero and six. Right now next value would be next value would be point, this is four times zero and six. This is 10 and this is five times zero and six. Right? So basically this is five times zero and six. So five times zero and 6. So this must be smaller than this now and this must be a little bigger. So pointed five times 0 and six. This value and this value we know now we can easily see our values here and this is basically our relative frequency, relative frequency. If I write correctly, relative frequency instagram, relative frequency, hissed a gram. Right, just we answered our be part. Now let us talk about C part which which were were answered as mean being the sum of values some of data divided by number of data in the reference of these group frequency term weekend writers, submission of I 12 N. F. I. X. Side divided by submission of I 12 N. I want to win. This is F. I. Right. So basically F I X. I would be submission as So we would we would we would like to take the middle values for the zero and 400. Middle values to 50 to 50. Multiply by 22 here. 7 50 multiply by 201. So 2 50 multiply by 20 to 7 50 multiply by 7 50 multiplied by 201. Right? And this value goes up to if I write roughly, this is 1500. Multiplied by 5500. Multiplying by multiply by this is 5500. Multiplied by 33994. And there's submission of frequencies which is which we have calculated as 3353843353884. Right? So basically the total value, if I calculated by roughly this is 11 319358 500. Which is divided by 3353884. So if I divide this, My answer would be roughly 33 75. Right? So basically our meanness mean value is 3375. So now we need to calculate our standard deviation So standard evasion first we calculate our variance which is our sigma square and under root of sigma squared standard deviation right? So sigma square would be sigma of f. I exercise square divided by irish to want I want to end can military so we can write 12 and right and values and submission of S I F I. And this is 12 and n minus X. Bar. So basically mean is considered an expert. So basically extra reach to power to right? So what would be that value? This is sigma square X question F I x e x I square means uh if I catch 22 multiply by 2 50 square rights, 22 multiply by 2 50 square and dot dot dot these are in the form of plaza and 7 50 multiplied by against 7 50 multiplied by again. If I write for this, 7 50 multiplied by 201 square and dot dot dot this value will come out as 55 if I write for this, but this is this is this is a this must be corrected. So this is 7 50 square, multiplied by 201. So 201 multiplied by 7 50 square. And again 5550 I fi right frequencies of 5500 square multiplied by that, that that is that is our 3994. Right? And sigma phi phi we all know sigma f i s 3353 884. And this is the whole value minus. This is 3375 square. Right now this value would be if I write this so roughly five calculated this is 4.6372. Multiply by 10 days to power 12 divided by 3353884 minus this is 3375 square. So 3375 square would be 11 390625. Right, So this whole value, if I roughly calculated will come out as this will come out as 24 three double 9.2 point 2566. Right? Which is sigma square. And we need to calculate our standard deviation standard deviation would be under root of this. Under root of sigma, Root of sigma's car, 24 3 double 9.56 is right. So this value will be confined to 492492.96 roughly calculated. So we have got our meaning standard aviation, so if I right there mean is equals to I mean if I write here correctly, mean is equals to 3375 33 75. And the standard deviation standard deviation if I write for it, This is basically 4 9, 2.96 now. So now in the deep point we need to calculate our probability distribution according to normal model. So first we first be uh if I want to put a point here here, we need to apply normal border distribution. So basically what is our normal distribution? Normal distribution is a distribution in which ex uh in which x is our random variable distributed in bell shaped car. Right? So basically, if I talk about the normal model, so this is basically something like this having probability function here, maybe PX or peach are So if I calculate according to PSR from this is just so it is distributed, something like this. Right? So if I draw for this, I will draw their also. So here the parameter judges score which is x minus mu divided by sigma. Where amusement and sigma is industry standard division and probability value is basically P X equals to one upon sigma. Underwrote to pay I. E. Raised to power minus X minus mu divided by sigma raised to power to and this is half right. So basically this is there so this is one upon sigma. Underwrote to pay I. E raised to power minus a chair is quite divided by two. Right? So basically this is PJ right? And this is basically minus verify. Right? So if I this is a normal moral distribution. So now if I see so we need to calculate each and every probability value and make our this table Right? So let us make the table again for it. So let's make the table again. So I will not calculate each and every particular value, I will directly write the values according to the table. So the table must be something like this and this is the table and if I write for this this is so we all know our exchanges, we need to directly calculate our probability now draw the table. So this must be broken and if I right here so Here will be worth the wait and here would be values right? So basically this is our worth of weight and these are having our values which of normal model values. So here normal model, if I write that would be better. And we start with 02499. Right? So basically this is 2.7 month multiplied by 10, raised to power -9. And this is 500 to 999 must be written as 7.19, multiplied by 10, raised to power minus seven. This is 1000 to 1499 must be caused to 7.3 and this is 7.19. Right? So basically this is multiplied by 10 days to power minus five. And this is 1500 2 99. This is 99 99 1999. This is zero point double 0 to 56 and this is 2000 22499 can be written as if I write for this, this is .03523. We are getting this value after putting this value in the acts in the terms of the ranges and this is 2499 and 2500 to 2999 can be written as 29990.18 point 1852. And this can be written as 2349 3009 can be written as 30090.37625. Now, 3500 to 3999 can be written as if I write .297. And this is the value 4000-4000-4499 can be written as if I write this is .0913. Right? And this must be raised to to increase that table. So if I increase that table it will come out as so increase that table. So this must be increased to this must exchange. Now this must also be increased right now. Meet this table. Right? And this also now let us perform other values to. So basically this is 4500 to 4 triple nine. And this is basically 225 $5004 line. Now what would be my value which are left? So this is basically 0.107. And this is Triple 0483. Right. So basically this is our table. So if I right if I write for this uh they use normal model to determine the proportion of basics. So basically this is proportional basics too. So this is our table proportion off off proportion of proportion of babies in babies in each class, babies and each class normal model, they will right now let us come to our next part which is our which is our butt compared the proportion predicted by normal modern era to the relative frequency found in part A right now let us compare right for e part we need to meet first our our normal values are so sorry, our frequency values. So this this this point at this point at this point this point this point must be met and if I meet meet this. So this will come out at this point. And this point And this point must be cover at this point. Again this point this point at this point. So basically Karpov has bell shaped bell shaped frequency frequency distribution curve, distribution curve, Right? And if I talk according to normal values. So first values started from this is very small and again it is it is a it is again increasing and let us talk about the greater values. Right? So instead of 4104 hair value is .37. Right, So something here and if I write for other values so pointed. So let us point that this value is here and other values are so this is maybe similar, right? For we are talking about for normal values. Red represent red represent here normal values. Right, normal values. Right? So basically here, this is point. If I write for this, this is point 18th, right? And this is .035. So basically greater than this, but this is smaller now, next value, if I right for this, this is .295. And here .297. So very similar. So some what? The values are similar. Right? If I made this right? Some of the values are similar. So if I write our first, sorry. D statements where he compared the proportion predicted by normal. So so the proportion proportions predicted where it did by normal model are almost similar, are almost similar to the frequency to frequency related distribution values. Right now, what is our F. Part? If I talk about F part F part is do you believe that normal model is effective in describing the worth weight of babies? Right. So I can write this normal. Yes. Normal model is effective. Normal model. It's effective No. In describing describing word awaits of babies, right? Hence we got all the answers and all the explanations. Thank you.

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