Making Predictions from Data

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Show your work for each problem.

1.
A regression line is $\hat{y} = 4x + 10$ . What is the predicted value when $x = 5$ ?
1. a)14
2. b)40
3. c)30
4. d)20
2.
The regression line for a data set is $\hat{y} = 3x + 12$ . Predict $\hat{y}$ for $x = 6$ .
3.
The data in a scatter plot has $x$ -values from $2$ to $10$ . For which $x$ -value is a prediction an interpolation?
1. a)12
2. b)7
3. c)15
4. d)0
4.
A plant's height in mm follows $\hat{y} = 2.5x + 40$ , where $x$ is the number of days (data from day 1 to day 10). Predict the height on day $4$ .
5.
A shop models its daily umbrella sales with $\hat{y} = 6x + 20$ , where $x$ is the rainfall in mm (data from 0 to 12 mm). Predict the sales on a day with $7$ mm of rain.
6.
Four data sets each have a regression line. Which correlation coefficient gives the most reliable predictions?
1. a)r = -0.95
2. b)r = 0.1
3. c)r = 0.25
4. d)r = 0.5
7.
A model predicts a test score with $\hat{y} = 4x + 18$ , where $x$ is hours of practice (data from 2 to 15 hours). For which $x$ is the predicted score $50$ ?
8.
Using $\hat{y} = 5x + 52$ ( $x$ = hours studied, $\hat{y}$ = test score), how many hours of study predict a score of $87$ ?
9.
A school fair models visitors with $\hat{y} = 14.6x + 23$ , where $x$ is the number of posters (data from 2 to 10 posters). Predict the number of visitors for $6$ posters, rounded to a whole number.
10.
The line $\hat{y} = 5x + 52$ was fitted to data from 1 to 8 hours of study. For 12 hours it predicts a score of $112$ out of $100$ . What is the problem?
1. a)The intercept should be 0
2. b)12 hours is outside the data, and a score above 100 is impossible
3. c)Nothing, the prediction is reliable
4. d)The slope should be negative
11.
While gaming, a phone's battery level follows $\hat{y} = 100 - 12x$ (percent), where $x$ is hours of gaming (data from 0 to 6 hours). Predict the battery level after $4.5$ hours.
12.
With the battery model $\hat{y} = 100 - 12x$ ( $x$ in hours, $\hat{y}$ in percent), after how many hours does the model predict a battery level of $40\%$ ?
13.
A regression model says Tom needs $5.6$ hours of study to reach his target score. Which plan makes the most sense?
1. a)Study 5 hours
2. b)Study about 6 hours
3. c)Study exactly 5.6 hours, not a minute more
4. d)Study 0.6 hours
14.
A regression line has slope $m = 2.5$ and passes through the point of means $(\bar{x}, \bar{y}) = (4, 30)$ . Predict $\hat{y}$ for $x = 6$ .
15.
A growth model for children aged 2 to 10 is $\hat{y} = 6x + 77$ (height in cm, age $x$ in years). A student uses it to predict the height of a 40-year-old.
16.
A regression line is $\hat{y} = 2.4x + 15.6$ . For which $x$ is the predicted value $39.6$ ?
17.
A class has two models for the test score: hours studied, $\hat{y} = 5x + 52$ with $r \approx 0.99$ , and hours of sleep, $\hat{y} = 2x + 59$ with $r \approx 0.21$ . Both are used for $x = 6$ hours.
18.
With $\hat{y} = 5x + 52$ ( $x$ = hours studied, data from 1 to 8 hours), Mia wants a score of at least $90$ . How many whole hours should she plan?