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The height of the softball when it travels 12 feet using the quadratic regression model is 5.53 foot.
<h3>What is the correlation coefficient?</h3>Correlation coefficient is used to calculate how strong the relationship is between the two variables.
When there is a statistical relationship between two or more variables, then they are said to be in correlation.
The table represents the distance and height for softball travels after being hit by the batter.
- Distance x (ft) Height y (ft)
- 0 5
- 2 25
- 4 37
- 6 42
- 8 34
- 10 26
- Mean 5 28.167
The mean of the data of distance is 5 and the mean of the data of height is 28.167. The correlation coefficient is 0.9938.
The quadratic regression model for this model is given as,
At the 12 feet, the value of height y is,
Hence, the height of the softball when it travels 12 feet using the quadratic regression model is 5.53 foot.
Learn more about the correlation coefficient here;
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The attached picture is a summary of all the six transformations you'd do.
Any change outside the f(x) notation impacts y-values of points on the graph.
Any changes inside the f(x) notation impacts x-values of points on the graph.
The trick is that the inside changes are usually the opposite of what you'd expect to have happen.
7. y=f(x)+8
This is an outside change. You're adding 8 to all the y-values of points on the graph. This will shift your entire graph up 8 units.
8. y=f(x+6)
This is an inside change. Because it says "+6", you want to think, "Ah! That means I'll actually subtract 6 from the x-value of every point on the graph." This graph is shifted 6 units to the left.
9. y=-f(x)
Inside change, impacts y-values. Every y-value will be given the opposite signs. Negatives become positive and positives become negative. This will flip your graph over the x-axis.
10. y = f(-x) + 5
Give this one a shot on your own first in a comment and I'll let you know how you did.
11. y = - 3 f(x-3)
There are three things happening. A negative on the outside, multiplying by 3 on the outside, and subtracting 3 inside. What will each of those do individually? Take a shot on this one and let me know what you think.
12. y = 1/2 f( 1/2 x )
Again, three changes. Try this one and let me know what you think. Remember multiplying by 1/2 inside really means you'll do the opposite of multiplying by 1/2.
