Listed below are the budgets (in millions of dollars) and the gross receipts (in

Question

Listed below are the budgets (in millions of dollars) and the gross receipts (in millions of dollars ) for randomly selected movies. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a =0.05. Is there sufficient evidence to conclude that there is a linear correlation between budgets and gross receipts? Do the results change if the actual budgets listed are s60,000,000, $90,000,000, $48,000,000, and so on? Budget (x) T60 T90 T48 T33T195 T98 T91 lo Gross (y) 61635357 650 14550 O What are the null and alternative hypotheses? O A. Hg : p=0 Hy: p0 O B. Hypt 0 H, p=0 o D. Hop=0 Hy: p

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Gross (Y)
Independent Variable: Budget (X)
Gross (Y) = -179.5998 + 3.7986969 Budget (X)
Sample size: 7
R (correlation coefficient) = 0.91351853
R-sq = 0.83451611
Estimate of error standard deviation: 98.551225

Parameter estimates:

Analysis of variance table for regression model:

Hence,

Null and alternative hypotheses: Option C is correct.

Scatterplot: Option B is correct.

r = 0.914

Test statistic (t) = 5.021

P - value = 0.004

Conclusion: Option B is correct.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -179.5998 76.190262 0 5 -2.357254 0.065 Slope 3.7986969 0.7565021 0 5 5.0213964 0.004

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