Question

In: Statistics and Probability

The data show the time intervals after an eruption​ (to the next​ eruption) of a certain...

The data show the time intervals after an eruption​ (to the next​ eruption) of a certain geyser. Find the regression​ equation, letting the first variable be the independent​ (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of 149 feet. Use a significance level of 0.05. Height​ (ft) 136 140 134 144 102 109 104 116 Interval after​ (min) 83 84 94 92 67 67 84 84.

What is the regression equation?

Solutions

Expert Solution

Sum of X = 985
Sum of Y = 655
Mean X = 123.125
Mean Y = 81.875
Sum of squares (SSX) = 2066.875
Sum of products (SP) = 862.125

Regression Equation = ŷ = bX + a

b = SP/SSX = 862.13/2066.88 = 0.4171

a = MY - bMX = 81.88 - (0.42*123.13) = 30.5177

ŷ = 0.4171X + 30.5177

X Values
∑ = 985
Mean = 123.125
∑(X - Mx)2 = SSx = 2066.875

Y Values
∑ = 655
Mean = 81.875
∑(Y - My)2 = SSy = 706.875

X and Y Combined
N = 8
∑(X - Mx)(Y - My) = 862.125

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 862.125 / √((2066.875)(706.875)) = 0.7133

The sample size is n=8, so then the number of degrees of freedom is df=n−2=8−2=6

The corresponding critical correlation value rc​ for a significance level of α=0.05, for a two-tailed test is:

rc​=0.707

Observe that in this case, the null hypothesis is rejected if ∣r∣>rc​=0.707.

As r>rc, so test is significant

Now for x=149,

ŷ = (0.4171*149) + 30.5177=92.6656


Related Solutions

The data show the time intervals after an eruption​ (to the next​ eruption) of a certain...
The data show the time intervals after an eruption​ (to the next​ eruption) of a certain geyser. Find the regression​ equation, letting the height of the current eruption be the explanatory variable​ (denoted by​ x). Then use this equation to determine the predicted length of the time interval after an eruption given that the current eruption has a height of 113feet. Height (ft), Interval after (min) 96 66 128 85 75 59 128 86 88 70 73 75 80 73...
The data show the time intervals after an eruption (to the next eruption) of a certain...
The data show the time intervals after an eruption (to the next eruption) of a certain geyser. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of 120 feet. Use a significance level of 0.05. Height (ft) Height (ft)   Interval after (min) 96   68 111   80 76   66 91   72 66   58 108   79 116   84 91  ...
The data show the time intervals after an eruption​ (to the next​ eruption) of a certain...
The data show the time intervals after an eruption​ (to the next​ eruption) of a certain geyser. Find the regression​ equation, letting the first variable be the independent​ (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of 126 feet. Use a significance level of 0.05. Height (ft)   Interval after (min) 84   76 122   77 78   67 108   87 73   61 105   77 122   87 78   70 What...
The data show the time intervals after an eruption​ (to the next​ eruption) of a certain...
The data show the time intervals after an eruption​ (to the next​ eruption) of a certain geyser. Find the regression​ equation, letting the first variable be the independent​ (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of 148 feet. Use a significance level of 0.05. Height (ft) Interval after (min) 136 83 140 84 134 94 144 92 102 67 109 67 104 84 116 84
The eruption height and the time interval after eruption of a geyser were measured and are...
The eruption height and the time interval after eruption of a geyser were measured and are shown below. Answer parts ​a-c. Height (x)   Interval after (y) 140   75 130   71 115   59 140   73 112   64 110   56 100   54 120   68 a. Find the value of the linear correlation coefficient r. b. Find the critical values of r from the table showing the critical values for the Pearson correlation coefficient using α=0.05 c. Is there sufficient evidence to conclude...
The eruption height and the time interval after eruption of a geyser were measured and are...
The eruption height and the time interval after eruption of a geyser were measured and are shown below. Answer parts ​a-c. Height​ (x) 125 135 85 95 100 95 115 105 Interval after​ (y) 58 62 40 45 47 48 57 50 a. Find the value of the linear correlation coefficient r. b. Find the critical values of r from the table showing the critical values for the Pearson correlation coefficient using alpha=0.05. c. Is there sufficient evidence to conclude...
For a certain river, suppose the drought length Y is the number of consecutive time intervals...
For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.409 for this random variable. (Round your answers to three decimal places.)(a) What is the probability that a drought lasts exactly 3 intervals? At most 3...
For a certain river, suppose the drought length Y is the number of consecutive time intervals...
For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.385 for this random variable. (Round your answers to three decimal places.) (a) What is the probability that a drought lasts exactly 3 intervals? At most...
Data from service records show that the time to repair a certain machine is normally distributed with a mean of 65 min
Data from service records show that the time to repair a certain machine is normally distributed with a mean of 65 min and a standard deviation of 5 min. Estimate how often it will take more than 75 min to repair a machine.
The data below shows the duration of eruption (in seconds) of a geyser in a national...
The data below shows the duration of eruption (in seconds) of a geyser in a national park and the height (in feet) of the eruptions for a typical day. Use Excel to find the best fit linear regression equation, where duration of eruption is the explanatory variable. Round the slope and intercept to one decimal place. Duration   Height 240   140 237   154 122   140 267   140 113   160 258   140 232   150 105   150 186   160 248   155 243   125...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT