Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. x 69 66 63 65 76 76 y 54 53 51 43 47 45 Verify that Se ≈ 4.739, a ≈ 67.050, b ≈ –0.263, and , ∑x =415, ∑y =293, ∑x2 =28,863, and ∑y2 =14,409, and find a 90% confidence interval for β and interpret its meaning. Round your final answers to three decimal places. answer choices: The 90% confidence interval for β is from –0.993 to 0.466 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –0.99 and 0.47. The 90% confidence interval for β is from –1.065 to 0.539 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.07 and 0.54. The 90% confidence interval for β is from –0.882 to 0.355 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –0.88 and 0.36. The 90% confidence interval for β is from –1.023 to 0.496 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.02 and 0.50. The 90% confidence interval for β is from –1.309 to 0.782 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.31 and 0.78.
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
x | 69 | 66 | 63 | 65 | 76 | 76 |
y | 54 | 53 | 51 | 43 | 47 | 45 |
Verify that Se ≈ 4.739, a ≈ 67.050, b ≈ –0.263, and , ∑x =415, ∑y =293, ∑x2 =28,863, and ∑y2 =14,409, and find a 90% confidence interval for β and interpret its meaning. Round your final answers to three decimal places.
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season
Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season.
n=6
The excel steps for regression is obtained as-
The steps taken to obtain the simple linear regression to determine the amount of time spent on homework can be predicted by amount of sleep is given as follows: -
- Enter the data in Excel spreadsheet [ x and y]
- Go to data>Go to data analysis>Select regression>click OK.
- Select Input Y Range>Select Input X Range>click Labels>click Ok
The output obtained is given as follows-
Regression Statistics | ||||||
Multiple R | 0.331 | |||||
R Square | 0.109 | |||||
Adjusted R Square | -0.113 | |||||
Standard Error | 4.739 | |||||
Observations | 6 | |||||
ANOVA | ||||||
df | SS | MS | F | Significance F | ||
Regression | 1 | 11.01801329 | 11.018013 | 0.490696 | 0.522220859 | |
Residual | 4 | 89.81532004 | 22.45383 | |||
Total | 5 | 100.8333333 | ||||
Coefficients | Standard Error | t Stat | P-value | Lower 90.0% | Upper 90.0% | |
Intercept | 67.050 | 26.078 | 2.571 | 0.062 | 11.457 | 122.644 |
x | -0.263 | 0.376 | -0.700 | 0.522 | -1.065 | 0.539 |
The table below shows the required calculation-
x | y | x2 | y2 | |
69 | 54 | 4761 | 2916 | |
66 | 53 | 4356 | 2809 | |
63 | 51 | 3969 | 2601 | |
65 | 43 | 4225 | 1849 | |
76 | 47 | 5776 | 2209 | |
76 | 45 | 5776 | 2025 | |
Total | 415 | 293 | 28863 | 14409 |
Thus,
is verified.
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