Studies suggest that women who smoke during pregnancy affect the birth weights of their newborn infants. To study this issue further, a sample of 10 women smokers were asked to estimate the average number of cigarettes they smoke per day. In the following table are their estimates and the birth weight (in kgs) of their child. Average Number of Cigarettes per day Birth Weight of Child (in kilograms) 22 2.91 16 3.27 4 3.68 19 3.14 42 2.32 8 3.82 12 3.45 30 2.95 14 3.00 16 3.68 (a) Find the least squares estimate of the linear model that expresses the birth weight of a child as a linear function of the average number of cigarettes mom consumes in a day. Use four decimals in each of your answers. Y^i = __________ +/- _____________ Xi (b) Find the value of the coefficient of determination, then complete its interpretation. r2= _____________ (use four decimals) The percentage of A. Variation B. Standard deviation C. The mean in A. the birth weight of the child B. The average number of cigarettes consumed in a day by the mother that is explained by its linear relationship with A. the birth weight of the child B. The average number of cigarettes consumed in a day by the mother is ________ %. (c) Interpret the meaning of the slope term in the estimate of the linear model, in the context of the data. As A. birth weight B. The number of cigarettes consumed in a day increases by A. by one on average B. by one kilogram the A. birth weight B. The number of cigarettes consumed in a day will A. will increase by an average of B. will decrease by an average of C. will increase by D. will decrease by ____________ (use four decimals)
Studies suggest that women who smoke during pregnancy affect the birth weights of their newborn infants. To study this issue further, a sample of 10 women smokers were asked to estimate the average number of cigarettes they smoke per day. In the following table are their estimates and the birth weight (in kgs) of their child.
| Average Number of Cigarettes per day | Birth Weight of Child (in kilograms) |
| 22 | 2.91 |
| 16 | 3.27 |
| 4 | 3.68 |
| 19 | 3.14 |
| 42 | 2.32 |
| 8 | 3.82 |
| 12 | 3.45 |
| 30 | 2.95 |
| 14 | 3.00 |
| 16 | 3.68 |
(a) Find the least squares estimate of the linear model that expresses the birth weight of a child as a linear
Y^i = __________ +/- _____________ Xi
(b) Find the value of the coefficient of determination, then complete its interpretation.
r2= _____________ (use four decimals)
The percentage of
A. Variation
B. Standard deviation
C. The mean
in
A. the birth weight of the child
B. The average number of cigarettes consumed in a day by the mother
that is explained by its linear relationship with
A. the birth weight of the child
B. The average number of cigarettes consumed in a day by the mother
is ________ %.
(c) Interpret the meaning of the slope term in the estimate of the linear model, in the context of the data.
As
A. birth weight
B. The number of cigarettes consumed in a day
increases by
A. by one on average
B. by one kilogram
the
A. birth weight
B. The number of cigarettes consumed in a day
will
(d) A expecting mother, who smokes, claims to smoke an average of 20 cigarettes in a day. Predict the weight of her newborn. Use two decimals in your answer.
(e) The weight of the child born to the expecting mother mentioned in (e) was 4.2 kilograms. Find the residual, use two decimals.
ei=_______________
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