Moondollars is a coffee franchise that has many coffee stores all over the world

Question

Moondollars is a coffee franchise that has many coffee stores all over the world. MoonDollars coffee is investigating a linear regression model to predict the annual income for a store based on the population of the city where the store is located. In the proposed regression model, annual store income is the response variable and population of the city is the explanatory variable. A random sample of 20 stores is selected and measurements are observed.

Population,Annual income
2850,2483,
900,1798,
2640,1560,
2180,1554,
1750,791,
480,-69,
1150,990,
1610,976,
1690,1719,
2670,2071,
2420,1845,
1230,1409,
2740,2361,
2970,1107,
3110,2356,
890,1015,
1050,1286,
2860,1211,
1400,1413,

2020,1889

Give the 95% prediction interval for the value x = 1,500. Give your answers as whole numbers. __ y^ __

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Annual Income
Independent Variable: Population
Annual Income = 615.79008 + 0.4555089 Population
Sample size: 20
R (correlation coefficient) = 0.62485127
R-sq = 0.39043911
Estimate of error standard deviation: 479.85593

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

95% prediction interval will be:

(259, 2339)

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 615.79008 280.32573 0 18 2.1966948 0.0414 Slope 0.4555089 0.13415056 0 18 3.3955049 0.0032

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